GB2622240A

GB2622240A - Blockchain state machine

Info

Publication number: GB2622240A
Application number: GB2213097.5A
Authority: GB
Inventors: Pagani Alessio; Burns Alec; Steven Wright Craig
Original assignee: Nchain Licensing AG
Current assignee: Nchain Licensing AG
Priority date: 2022-09-08
Filing date: 2022-09-08
Publication date: 2024-03-13
Also published as: WO2024052053A1; GB202213097D0

Abstract

A computer-implemented method for representing a state machine using a blockchain. A first party generates transactions representing all possible states of the state machine, including an initial transaction comprising a first output. Subsequent transactions are generated until each possible state through which the state machine can transition has been represented by a transaction, wherein each subsequent transaction comprises a respective input referencing an output of an earlier transaction and a respective output. The transactions are sent to a second party who implements the state machine and sends the corresponding transaction to a blockchain node for publication to the blockchain. A third party can re-play the state sequence by obtaining the transactions from the blockchain. The first party can map the transactions onto nodes of a state graph. The first party may be the second party.

Description

BLOCKCHAIN STATE MACHINE

TECHNICAL FIELD

The present disclosure relates to representing a state machine using blockchain transactions.

BACKGROUND

A blockchain refers to a form of distributed data structure, wherein a duplicate copy of the blockchain is maintained at each of a plurality of nodes in a distributed peer-to-peer (P2P) network (referred to below as a "blockchain network") and widely publicised. The blockchain comprises a chain of blocks of data, wherein each block comprises one or more transactions. Each transaction, other than so-called "coinbase transactions", points back to a preceding transaction in a sequence which may span one or more blocks going back to one or more coinbase transactions. Coinbase transactions are discussed further below. Transactions that are submitted to the blockchain network are included in new blocks. New blocks are created by a process often referred to as "mining", which involves each of a plurality of the nodes competing to perform "proof-of-work", i.e. solving a cryptographic puzzle based on a representation of a defined set of ordered and validated pending transactions waiting to be included in a new block of the blockchain. It should be noted that the blockchain may be pruned at some nodes, and the publication of blocks can be achieved through the publication of mere block headers.

The transactions in the blockchain may be used for one or more of the following purposes: to convey a digital asset (i.e. a number of digital tokens), to order a set of entries in a virtualised ledger or registry, to receive and process timestamp entries, and/or to time-order index pointers. A blockchain can also be exploited in order to layer additional functionality on top of the blockchain. For example blockchain protocols may allow for storage of additional user data or indexes to data in a transaction. There is no pre-specified limit to the maximum data capacity that can be stored within a single transaction, and therefore increasingly more complex data can be incorporated. For instance this may be used to store an electronic document in the blockchain, or audio or video data.

Nodes of the blockchain network (which are often referred to as "miners") perform a distributed transaction registration and verification process, which will be described in more detail later. In summary, during this process a node validates transactions and inserts them into a block template for which they attempt to identify a valid proof-of-work solution. Once a valid solution is found, a new block is propagated to other nodes of the network, thus enabling each node to record the new block on the blockchain. In order to have a transaction recorded in the blockchain, a user (e.g. a blockchain client application) sends the transaction to one of the nodes of the network to be propagated. Nodes which receive the transaction may race to find a proof-of-work solution incorporating the validated transaction into a new block. Each node is configured to enforce the same node protocol, which will include one or more conditions for a transaction to be valid. Invalid transactions will not be propagated nor incorporated into blocks. Assuming the transaction is validated and thereby accepted onto the blockchain, then the transaction (including any user data) will thus remain registered and indexed at each of the nodes in the blockchain network as an immutable public record.

The node who successfully solved the proof-of-work puzzle to create the latest block is typically rewarded with a new transaction called the "coinbase transaction" which distributes an amount of the digital asset, i.e. a number of tokens. The detection and rejection of invalid transactions is enforced by the actions of competing nodes who act as agents of the network and are incentivised to report and block malfeasance. The widespread publication of information allows users to continuously audit the performance of nodes. The publication of the mere block headers allows participants to ensure the ongoing integrity of the blockchain.

In an "output-based" model (sometimes referred to as a UTXO-based model), the data structure of a given transaction comprises one or more inputs and one or more outputs. Any spendable output comprises an element specifying an amount of the digital asset that is derivable from the proceeding sequence of transactions. The spendable output is sometimes referred to as a UTXO ("unspent transaction output"). The output may further comprise a locking script specifying a condition for the future redemption of the output. A locking script is a predicate defining the conditions necessary to validate and transfer digital tokens or assets. Each input of a transaction (other than a coinbase transaction) comprises a pointer (i.e. a reference) to such an output in a preceding transaction, and may further comprise an unlocking script for unlocking the locking script of the pointed-to output. So consider a pair of transactions, call them a first and a second transaction (or "target" transaction). The first transaction comprises at least one output specifying an amount of the digital asset, and comprising a locking script defining one or more conditions of unlocking the output. The second, target transaction comprises at least one input, comprising a pointer to the output of the first transaction, and an unlocking script for unlocking the output of the first transaction.

In such a model, when the second, target transaction is sent to the blockchain network to be propagated and recorded in the blockchain, one of the criteria for validity applied at each node will be that the unlocking script meets all of the one or more conditions defined in the locking script of the first transaction. Another will be that the output of the first transaction has not already been redeemed by another, earlier valid transaction. Any node that finds the target transaction invalid according to any of these conditions will not propagate it (as a valid transaction, but possibly to register an invalid transaction) nor include it in a new block to be recorded in the blockchain.

An alternative type of transaction model is an account-based model. In this case each transaction does not define the amount to be transferred by referring back to the UTXO of a preceding transaction in a sequence of past transactions, but rather by reference to an absolute account balance. The current state of all accounts is stored by the nodes separate to the blockchain and is updated constantly.

SUMMARY

Finite-state machines are mathematical models used for representing programs and computations in systems that consist of a finite number of states, and that are always in exactly a single state. When transitioning from one state to another, typically an event is logged so that any interested party knows exactly when (and perhaps why) a transition is triggered.

The present disclosure recognises that, within a state machine, states and transitions between states can be represented using blockchain transactions. Therefore, the blockchain can be used to represent finite-state machines.

According to one aspect disclosed herein, there is provided a computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, and wherein the method is performed by a first party and comprises: generating a plurality of transactions representing all possible states of the state machine, said generating comprising: generating an initial transaction, wherein the initial transaction represents an initial state of the state machine and comprises a respective first output; for each respective state to which the initial state can transaction, generating a respective transaction, wherein the respective transaction represents the respective state and comprises a respective input referencing the respective first output of the initial transaction, and a respective spendable output; repeating a process of generating respective transactions representing respective states until each possible state through which the state machine can transition has been represented by a respective transaction, wherein each respective transaction comprises a respective input that references a respective first output of a previous respective transaction that represents a previous state from which the state machine can transition to reach the respective state represented by the respective transaction, and a respective first output; and sending the plurality of transactions available to a second party, wherein the second party operates a device configured to implement the state machine.

According to another aspect disclosed herein, there is provided a computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state ca n transition to one or more respective states, wherein the method is performed by a second party, wherein the second party comprises a device configured to implement the state machine, and wherein the method comprises: receiving a plurality of transactions representing the state machine, wherein the plurality of transactions are generated by comprising: generating an initial transaction, wherein the initial transaction represents an initial state of the state machine and comprises a respective first output; for each respective state to which the initial state can transaction, generating a respective transaction, wherein the respective transaction represents the respective state and comprises a respective input referencing the respective first output of the initial transaction, and a respective spendable output; and repeating a process of generating respective transactions representing respective states until each possible state through which the state machine can transition has been represented by a respective transaction, wherein each respective transaction comprises a respective input that references a respective first output of a previous respective transaction that represents a previous state from which the state machine can transition to reach the respective state represented by the respective transaction, and a respective first output; in response to a respective transition from a respective state to a respective next state of the state machine, sending the respective transaction representing the respective next state to one or more blockchain nodes for publishing on the blockchain.

According to another aspect disclosed herein, there is provided a computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, and wherein the method is performed by a first party and comprises: generating a state graph representing a plurality of ordered sequences of states through which the state machine can transition, wherein the state graph comprises a plurality of nodes and a plurality of edges, each respective node representing a respective state and each respective edge connecting a respective previous node to a respective next node represents a respective transaction from a respective previous state to a respective next state, wherein each respective node can be traced back to an initial node representing an initial state, wherein each respective node can be a respective parent node to one or more respective child nodes, and wherein each respective child node can be a respective child node of one or more respective parent nodes; generating a plurality of transactions, wherein each transaction is mapped to a respective node of the state graph, and wherein each respective edge connecting a respective previous node to a respective next node is represented by a respective reference to a respective previous transaction mapped to the respective previous node by a respective next transaction mapped to the respective next node; and sending the plurality of transactions available to a device configured to implement the state machine.

According to another aspect disclosed herein, there is provided a computer-implemented method of re-playing a state machine, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, wherein a blockchain comprises a chain of respective transactions, each respective transaction representing a respective state of the state machine, wherein the chain of transactions comprises an initial transaction representing an initial state of the state machine, and wherein the method is performed by a third party and comprises: obtaining each respective transaction in the chain of transactions; and determining a sequence of respective states through which the state machine has transitioned based on the respective states represented by the respective transactions in the chain of transactions.

Embodiments of the present disclosure provide a novel methodology for representing and executing finite-state machines using the blockchain. These finite-state machines may be represented as an overlay directed graph of unpublished transactions and executed as a chain of published transactions. The published chain of states inherits the same features that characterise all blockchain transactions, including transparency and immutability. The result is a finite-state machine that may be created and deployed locally, and whose execution path is stored immutably on the blockchain, provably auditable and re-playable.

Generating the transactions (representing all possible states of the state machine) in advance and supplying them to the device that implements the state machine has several advantages. For instance, the device is not responsible for generating the transactions, which in turn means less resources are consumed by the device. This is particularly beneficial for resource-constrained devices. Moreover, in some examples, the transactions are sent to the device pre-signed. Therefore the private key(s) required to sign the transactions do not have to be transmitted to, or stored by, the device. This improves security of the system. As a particular example, if the device is hacked or corrupted, the private key used to sign the transactions will not be compromised. Pre-signing the transactions is also particularly beneficial for resource-constrained devices.

BRIEF DESCRIPTION OF THE DRAWINGS

To assist understanding of embodiments of the present disclosure and to show how such embodiments may be put into effect, reference is made, by way of example only, to the accompanying drawings in which: Figure 1 is a schematic block diagram of a system for implementing a blockchain; Figure 2 schematically illustrates some examples of transactions which may be recorded in a blockchain; Figure 3 schematically illustrates an example finite-state machine with two states (A and B), where from each state it is possible to stay in the current state (transactions 2 and 4) or change to the other state (transactions 1 and 3); Figure 4 schematically illustrates an example system for implementing a blockchain-based state machine; Figure 5 schematically illustrates an example finite-state machine with five states; Figure 6 schematically illustrates a blockchain state machine with 5 states (state D is replicated), equivalent to the state machine of Figure 5, where the blockchain state machine is composed of unpublished transactions; Figure 7 schematically illustrates a sequence of states visited by the state machine of Figure 6 (A -> C-> D), where the visited states are the only transactions published on-chain; Figure 8 schematically illustrates two examples of state machines with loops, (I) 1 loop A-> B-> C-> A, (II) 3 loops A-> B-> A, A-> A, B-> B; and Figure 9 schematically illustrates two example blockchain state machines replicating the loop patterns of Figure 8.

DETAILED DESCRIPTION OF EMBODIMENTS

1. EXAMPLE SYSTEM OVERVIEW Figure 1 shows an example system 100 for implementing a blockchain 150. The system 100 may comprise a packet-switched network 101, typically a wide-area internetwork such as the Internet. The packet-switched network 101 comprises a plurality of blockchain nodes 104 that may be arranged to form a peer-to-peer (P2P) network 106 within the packet-switched network 101. Whilst not illustrated, the blockchain nodes 104 may be arranged as a near-complete graph. Each blockchain node 104 is therefore highly connected to other blockchain nodes 104.

Each blockchain node 104 comprises computer equipment of a peer, with different ones of the nodes 104 belonging to different peers. Each blockchain node 104 comprises processing apparatus comprising one or more processors, e.g. one or more central processing units (CPUs), accelerator processors, application specific processors and/or field programmable gate arrays (FPGAs), and other equipment such as application specific integrated circuits (ASICs). Each node also comprises memory, i.e. computer-readable storage in the form of a non-transitory computer-readable medium or media. The memory may comprise one or more memory units employing one or more memory media, e.g. a magnetic medium such as a hard disk; an electronic medium such as a solid-state drive (SSD), flash memory or EEPROM; and/or an optical medium such as an optical disk drive.

The blockchain 150 comprises a chain of blocks of data 151, wherein a respective copy of the blockchain 150 is maintained at each of a plurality of blockchain nodes 104 in the distributed or blockchain network 106. As mentioned above, maintaining a copy of the blockchain 150 does not necessarily mean storing the blockchain 150 in full. Instead, the blockchain 150 may be pruned of data so long as each blockchain node 150 stores the block header (discussed below) of each block 151. Each block 151 in the chain comprises one or more transactions 152, wherein a transaction in this context refers to a kind of data structure. The nature of the data structure will depend on the type of transaction protocol used as part of a transaction model or scheme. A given blockchain will use one particular transaction protocol throughout. In one common type of transaction protocol, the data structure of each transaction 152 comprises at least one input and at least one output. Each output specifies an amount representing a quantity of a digital asset as property, an example of which is a user 103 to whom the output is cryptographically locked (requiring a signature or other solution of that user in order to be unlocked and thereby redeemed or spent). Each input points back to the output of a preceding transaction 152, thereby linking the transactions.

Each block 151 also comprises a block pointer 155 pointing back to the previously created block 151 in the chain so as to define a sequential order to the blocks 151. Each transaction 152 (other than a coinbase transaction) comprises a pointer back to a previous transaction so as to define an order to sequences of transactions (N.B. sequences of transactions 152 are allowed to branch). The chain of blocks 151 goes all the way back to a genesis block (Gb) 153 which was the first block in the chain. One or more original transactions 152 early on in the chain 150 pointed to the genesis block 153 rather than a preceding transaction.

Each of the blockchain nodes 104 is configured to forward transactions 152 to other blockchain nodes 104, and thereby cause transactions 152 to be propagated throughout the network 106. Each blockchain node 104 is configured to create blocks 151 and to store a respective copy of the same blockchain 150 in their respective memory. Each blockchain node 104 also maintains an ordered set (or "pool") 154 of transactions 152 waiting to be incorporated into blocks 151. The ordered pool 154 is often referred to as a "mempool". This term herein is not intended to limit to any particular blockchain, protocol or model. It refers to the ordered set of transactions which a node 104 has accepted as valid and for which the node 104 is obliged not to accept any other transactions attempting to spend the same output.

In a given present transaction 152j, the (or each) input comprises a pointer referencing the output of a preceding transaction 152i in the sequence of transactions, specifying that this output is to be redeemed or "spent" in the present transaction 152j. Spending or redeeming does not necessarily imply transfer of a financial asset, though that is certainly one common application. More generally spending could be described as consuming the output, or assigning it to one or more outputs in another, onward transaction. In general, the preceding transaction could be any transaction in the ordered set 154 or any block 151. The preceding transaction 152i need not necessarily exist at the time the present transaction 152j is created or even sent to the network 106, though the preceding transaction 152i will need to exist and be validated in order for the present transaction to be valid. Hence "preceding" herein refers to a predecessor in a logical sequence linked by pointers, not necessarily the time of creation or sending in a temporal sequence, and hence it does not necessarily exclude that the transactions 152i, 152j be created or sent out-of-order (see discussion below on orphan transactions). The preceding transaction 152i could equally be called the antecedent or predecessor transaction.

The input of the present transaction 152j also comprises the input authorisation, for example the signature of the user 103a to whom the output of the preceding transaction 152i is locked. In turn, the output of the present transaction 152j can be cryptographically locked to a new user or entity 103b. The present transaction 152j can thus transfer the amount defined in the input of the preceding transaction 152i to the new user or entity 103b as defined in the output of the present transaction 152j. In some cases a transaction 152 may have multiple outputs to split the input amount between multiple users or entities (one of whom could be the original user or entity 103a in order to give change). In some cases a transaction can also have multiple inputs to gather together the amounts from multiple outputs of one or more preceding transactions, and redistribute to one or more outputs of the current transaction.

According to an output-based transaction protocol such as bitcoin, when a party 103, such as an individual user or an organization, wishes to enact a new transaction 152j (either manually or by an automated process employed by the party), then the enacting party sends the new transaction from its computer terminal 102 to a recipient. The enacting party or the recipient will eventually send this transaction to one or more of the blockchain nodes 104 of the network 106 (which nowadays are typically servers or data centres, but could in principle be other user terminals). It is also not excluded that the party 103 enacting the new transaction 152j could send the transaction directly to one or more of the blockchain nodes 104 and, in some examples, not to the recipient. A blockchain node 104 that receives a transaction checks whether the transaction is valid according to a blockchain node protocol which is applied at each of the blockchain nodes 104. The blockchain node protocol typically requires the blockchain node 104 to check that a cryptographic signature in the new transaction 152j matches the expected signature, which depends on the previous transaction 152i in an ordered sequence of transactions 152. In such an output-based transaction protocol, this may comprise checking that the cryptographic signature or other authorisation of the party 103 included in the input of the new transaction 152j matches a condition defined in the output of the preceding transaction 152i which the new transaction spends (or "assigns"), wherein this condition typically comprises at least checking that the cryptographic signature or other authorisation in the input of the new transaction 152j unlocks the output of the previous transaction 152i to which the input of the new transaction is linked to. The condition may be at least partially defined by a script included in the output of the preceding transaction 152i. Alternatively it could simply be fixed by the blockchain node protocol alone, or it could be due to a combination of these. Either way, if the new transaction 152j is valid, the blockchain node 104 forwards it to one or more other blockchain nodes 104 in the blockchain network 106. These other blockchain nodes 104 apply the same test according to the same blockchain node protocol, and so forward the new transaction 152j on to one or more further nodes 104, and so forth. In this way the new transaction is propagated throughout the network of blockchain nodes 104.

In an output-based model, the definition of whether a given output (e.g. UTXO) is assigned (or "spent") is whether it has yet been validly redeemed by the input of another, onward transaction 152j according to the blockchain node protocol. Another condition for a transaction to be valid is that the output of the preceding transaction 152i which it attempts to redeem has not already been redeemed by another transaction. Again if not valid, the transaction 152j will not be propagated (unless flagged as invalid and propagated for alerting) or recorded in the blockchain 150. This guards against double-spending whereby the transactor tries to assign the output of the same transaction more than once. An account-based model on the other hand guards against double-spending by maintaining an account balance. Because again there is a defined order of transactions, the account balance has a single defined state at any one time.

In addition to validating transactions, blockchain nodes 104 also race to be the first to create blocks of transactions in a process commonly referred to as mining, which is supported by "proof-of-work". At a blockchain node 104, new transactions are added to an ordered pool 154 of valid transactions that have not yet appeared in a block 151 recorded on the blockchain 150. The blockchain nodes then race to assemble a new valid block 151 of transactions 152 from the ordered set of transactions 154 by attempting to solve a cryptographic puzzle. Typically this comprises searching for a "nonce" value such that when the nonce is concatenated with a representation of the ordered pool of pending transactions 154 and hashed, then the output of the hash meets a predetermined condition.

E.g. the predetermined condition may be that the output of the hash has a certain predefined number of leading zeros. Note that this is just one particular type of proof-ofwork puzzle, and other types are not excluded. A property of a hash function is that it has an unpredictable output with respect to its input. Therefore this search can only be performed by brute force, thus consuming a substantive amount of processing resource at each blockchain node 104 that is trying to solve the puzzle.

The first blockchain node 104 to solve the puzzle announces this to the network 106, providing the solution as proof which can then be easily checked by the other blockchain nodes 104 in the network (once given the solution to a hash it is straightforward to check that it causes the output of the hash to meet the condition). The first blockchain node 104 propagates a block to a threshold consensus of other nodes that accept the block and thus enforce the protocol rules. The ordered set of transactions 154 then becomes recorded as a new block 151 in the blockchain 150 by each of the blockchain nodes 104. A block pointer 155 is also assigned to the new block 151n pointing back to the previously created block 151n-1 in the chain. The significant amount of effort, for example in the form of hash, required to create a proof-of-work solution signals the intent of the first node 104 to follow the rules of the blockchain protocol. Such rules include not accepting a transaction as valid if it spends or assigns the same output as a previously validated transaction, otherwise known as double-spending. Once created, the block 151 cannot be modified since it is recognized and maintained at each of the blockchain nodes 104 in the blockchain network 106. The block pointer 155 also imposes a sequential order to the blocks 151. Since the transactions 152 are recorded in the ordered blocks at each blockchain node 104 in a network 106, this therefore provides an immutable public ledger of the transactions.

Note that different blockchain nodes 104 racing to solve the puzzle at any given time may be doing so based on different snapshots of the pool of yet-to-be published transactions 154 at any given time, depending on when they started searching for a solution or the order in which the transactions were received. Whoever solves their respective puzzle first defines which transactions 152 are included in the next new block 151n and in which order, and the current pool 154 of unpublished transactions is updated. The blockchain nodes 104 then continue to race to create a block from the newly-defined ordered pool of unpublished transactions 154, and so forth. A protocol also exists for resolving any "fork" that may arise, which is where two blockchain nodes104 solve their puzzle within a very short time of one another such that a conflicting view of the blockchain gets propagated between nodes 104. In short, whichever prong of the fork grows the longest becomes the definitive blockchain 150. Note this should not affect the users or agents of the network as the same transactions will appear in both forks.

According to the bitcoin blockchain (and most other blockchains) a node that successfully constructs a new block 104 is granted the ability to newly assign an additional, accepted amount of the digital asset in a new special kind of transaction which distributes an additional defined quantity of the digital asset (as opposed to an inter-agent, or inter-user transaction which transfers an amount of the digital asset from one agent or user to another). This special type of transaction is usually referred to as a "coinbase transaction", but may also be termed an "initiation transaction" or "generation transaction". It typically forms the first transaction of the new block 151n. The proof-of-work signals the intent of the node that constructs the new block to follow the protocol rules allowing this special transaction to be redeemed later. The blockchain protocol rules may require a maturity period, for example 100 blocks, before this special transaction may be redeemed. Often a regular (non-generation) transaction 152 will also specify an additional transaction fee in one of its outputs, to further reward the blockchain node 104 that created the block 151n in which that transaction was published. This fee is normally referred to as the "transaction fee", and is discussed blow.

Due to the resources involved in transaction validation and publication, typically at least each of the blockchain nodes 104 takes the form of a server comprising one or more physical server units, or even whole a data centre. However in principle any given blockchain node 104 could take the form of a user terminal or a group of user terminals networked together.

The memory of each blockchain node 104 stores software configured to run on the processing apparatus of the blockchain node 104 in order to perform its respective role or roles and handle transactions 152 in accordance with the blockchain node protocol. It will be understood that any action attributed herein to a blockchain node 104 may be performed by the software run on the processing apparatus of the respective computer equipment. The node software may be implemented in one or more applications at the application layer, or a lower layer such as the operating system layer or a protocol layer, or any combination of these.

Also connected to the network 101 is the computer equipment 102 of each of a plurality of parties 103 in the role of consuming users. These users may interact with the blockchain network 106 but do not participate in validating transactions or constructing blocks. Some of these users or agents 103 may act as senders and recipients in transactions. Other users may interact with the blockchain 150 without necessarily acting as senders or recipients. For instance, some parties may act as storage entities that store a copy of the blockchain 150 (e.g. having obtained a copy of the blockchain from a blockchain node 104).

Some or all of the parties 103 may be connected as part of a different network, e.g. a network overlaid on top of the blockchain network 106. Users of the blockchain network (often referred to as "clients") may be said to be part of a system that includes the blockchain network 106; however, these users are not blockchain nodes 104 as they do not perform the roles required of the blockchain nodes. Instead, each party 103 may interact with the blockchain network 106 and thereby utilize the blockchain 150 by connecting to (i.e. communicating with) a blockchain node 106. Two parties 103 and their respective equipment 102 are shown for illustrative purposes: a first party 103a and his/her respective computer equipment 102a, and a second party 103b and his/her respective computer equipment 102b. It will be understood that many more such parties 103 and their respective computer equipment 102 may be present and participating in the system 100, but for convenience they are not illustrated. Each party 103 may be an individual or an organization. Purely by way of illustration the first party 103a is referred to herein as Alice and the second party 103b is referred to as Bob, but it will be appreciated that this is not limiting and any reference herein to Alice or Bob may be replaced with "first party" and "second "party" respectively.

The computer equipment 102 of each party 103 comprises respective processing apparatus comprising one or more processors, e.g. one or more CPUs, GPUs, other accelerator processors, application specific processors, and/or FPGAs. The computer equipment 102 of each party 103 further comprises memory, i.e. computer-readable storage in the form of a non-transitory computer-readable medium or media. This memory may comprise one or more memory units employing one or more memory media, e.g. a magnetic medium such as hard disk; an electronic medium such as an SSD, flash memory or EEPROM; and/or an optical medium such as an optical disc drive. The memory on the computer equipment 102 of each party 103 stores software comprising a respective instance of at least one client application 105 arranged to run on the processing apparatus. It will be understood that any action attributed herein to a given party 103 may be performed using the software run on the processing apparatus of the respective computer equipment 102. The computer equipment 102 of each party 103 comprises at least one user terminal, e.g. a desktop or laptop computer, a tablet, a smartphone, or a wearable device such as a smartwatch. The computer equipment 102 of a given party 103 may also comprise one or more other networked resources, such as cloud computing resources accessed via the user terminal.

The client application 105 may be initially provided to the computer equipment 102 of any given party 103 on suitable computer-readable storage medium or media, e.g. downloaded from a server, or provided on a removable storage device such as a removable SSD, flash memory key, removable EEPROM, removable magnetic disk drive, magnetic floppy disk or tape, optical disk such as a CD or DVD ROM, or a removable optical drive, etc. The client application 105 comprises at least a "wallet" function. This has two main functionalities. One of these is to enable the respective party 103 to create, authorise (for example sign) and send transactions 152 to one or more bitcoin nodes 104 to then be propagated throughout the network of blockchain nodes 104 and thereby included in the blockchain 150. The other is to report back to the respective party the amount of the digital asset that he or she currently owns. In an output-based system, this second functionality comprises collating the amounts defined in the outputs of the various 152 transactions scattered throughout the blockchain 150 that belong to the party in question.

Note: whilst the various client functionality may be described as being integrated into a given client application 105, this is not necessarily limiting and instead any client functionality described herein may instead be implemented in a suite of two or more distinct applications, e.g. interfacing via an API, or one being a plug-in to the other. More generally the client functionality could be implemented at the application layer or a lower layer such as the operating system, or any combination of these. The following will be described in terms of a client application 105 but it will be appreciated that this is not limiting.

The instance of the client application or software 105 on each computer equipment 102 is operatively coupled to at least one of the blockchain nodes 104 of the network 106. This enables the wallet function of the client 105 to send transactions 152 to the network 106. The client 105 is also able to contact blockchain nodes 104 in order to query the blockchain 150 for any transactions of which the respective party 103 is the recipient (or indeed inspect other parties' transactions in the blockchain 150, since in embodiments the blockchain 150 is a public facility which provides trust in transactions in part through its public visibility). The wallet function on each computer equipment 102 is configured to formulate and send transactions 152 according to a transaction protocol. As set out above, each blockchain node 104 runs software configured to validate transactions 152 according to the blockchain node protocol, and to forward transactions 152 in order to propagate them throughout the blockchain network 106. The transaction protocol and the node protocol correspond to one another, and a given transaction protocol goes with a given node protocol, together implementing a given transaction model. The same transaction protocol is used for all transactions 152 in the blockchain 150. The same node protocol is used by all the nodes 104 in the network 106.

When a given party 103, say Alice, wishes to send a new transaction 152j to be included in the blockchain 150, then she formulates the new transaction in accordance with the relevant transaction protocol (using the wallet function in her client application 105). She then sends the transaction 152 from the client application 105 to one or more blockchain nodes 104 to which she is connected. E.g. this could be the blockchain node 104 that is best connected to Alice's computer 102. When any given blockchain node 104 receives a new transaction 152j, it handles it in accordance with the blockchain node protocol and its respective role. This comprises first checking whether the newly received transaction 152j meets a certain condition for being "valid", examples of which will be discussed in more detail shortly. In some transaction protocols, the condition for validation may be configurable on a per-transaction basis by scripts included in the transactions 152.

Alternatively the condition could simply be a built-in feature of the node protocol, or be defined by a combination of the script and the node protocol.

On condition that the newly received transaction 152j passes the test for being deemed valid (i.e. on condition that it is "validated"), any blockchain node 104 that receives the transaction 152j will add the new validated transaction 152 to the ordered set of transactions 154 maintained at that blockchain node 104. Further, any blockchain node 104 that receives the transaction 152j will propagate the validated transaction 152 onward to one or more other blockchain nodes 104 in the network 106. Since each blockchain node 104 applies the same protocol, then assuming the transaction 152j is valid, this means it will soon be propagated throughout the whole network 106.

Once admitted to the ordered pool of pending transactions 154 maintained at a given blockchain node 104, that blockchain node 104 will start competing to solve the proof-ofwork puzzle on the latest version of their respective pool of 154 including the new transaction 152 (recall that other blockchain nodes 104 may be trying to solve the puzzle based on a different pool of transactions154, but whoever gets there first will define the set of transactions that are included in the latest block 151. Eventually a blockchain node 104 will solve the puzzle for a part of the ordered pool 154 which includes Alice's transaction 152j). Once the proof-of-work has been done for the pool 154 including the new transaction 152j, it immutably becomes part of one of the blocks 151 in the blockchain 150. Each transaction 152 comprises a pointer back to an earlier transaction, so the order of the transactions is also immutably recorded.

Different blockchain nodes 104 may receive different instances of a given transaction first and therefore have conflicting views of which instance is 'valid' before one instance is published in a new block 151, at which point all blockchain nodes 104 agree that the published instance is the only valid instance. If a blockchain node 104 accepts one instance as valid, and then discovers that a second instance has been recorded in the blockchain 150 then that blockchain node 104 must accept this and will discard (i.e. treat as invalid) the instance which it had initially accepted (i.e. the one that has not been published in a block 151).

An alternative type of transaction protocol operated by some blockchain networks may be referred to as an "account-based" protocol, as part of an account-based transaction model. In the account-based case, each transaction does not define the amount to be transferred by referring back to the UTXO of a preceding transaction in a sequence of past transactions, but rather by reference to an absolute account balance. The current state of all accounts is stored, by the nodes of that network, separate to the blockchain and is updated constantly. In such a system, transactions are ordered using a running transaction tally of the account (also called the "position"). This value is signed by the sender as part of their cryptographic signature and is hashed as part of the transaction reference calculation. In addition, an optional data field may also be signed the transaction. This data field may point back to a previous transaction, for example if the previous transaction ID is included in the data field.

2. UTXO-BASED MODEL Figure 2 illustrates an example transaction protocol. This is an example of a UTXO-based protocol. A transaction 152 (abbreviated "Tx") is the fundamental data structure of the blockchain 150 (each block 151 comprising one or more transactions 152). The following will be described by reference to an output-based or "UTXO" based protocol. However, this is not limiting to all possible embodiments. Note that while the example UTXO-based protocol is described with reference to bitcoin, it may equally be implemented on other example blockchain networks.

In a UTXO-based model, each transaction ("Tx") 152 comprises a data structure comprising one or more inputs 202, and one or more outputs 203. Each output 203 may comprise an unspent transaction output (UTXO), which can be used as the source for the input 202 of another new transaction (if the UTXO has not already been redeemed). The UTXO includes a value specifying an amount of a digital asset. This represents a set number of tokens on the distributed ledger. The UTXO may also contain the transaction ID of the transaction from which it came, amongst other information. The transaction data structure may also comprise a header 201, which may comprise an indicator of the size of the input field(s) 202 and output field(s) 203. The header 201 may also include an ID of the transaction. In embodiments the transaction ID is the hash of the transaction data (excluding the transaction ID itself) and stored in the header 201 of the raw transaction 152 submitted to the nodes 104.

Say Alice 103a wishes to create a transaction 152j transferring an amount of the digital asset in question to Bob 103b. In Figure 2 Alice's new transaction 1521 is labelled "Tvz". It takes an amount of the digital asset that is locked to Alice in the output 203 of a preceding transaction 152i in the sequence, and transfers at least some of this to Bob. The preceding transaction 152i is labelled "Txo" in Figure 2. Txoand Txl are just arbitrary labels. They do not necessarily mean that Trois the first transaction in the blockchain 151, nor that Tx] is the immediate next transaction in the pool 154. Tx/ could point back to any preceding (i.e. antecedent) transaction that still has an unspent output 203 locked to Alice.

The preceding transaction Tx° may already have been validated and included in a block 151 of the blockchain 150 at the time when Alice creates her new transaction TKI, or at least by the time she sends it to the network 106. It may already have been included in one of the blocks 151 at that time, or it may be still waiting in the ordered set 154 in which case it will soon be included in a new block 151. Alternatively Ixo and Tv/ could be created and sent to the network 106 together, or Txo could even be sent after Tx/ if the node protocol allows for buffering "orphan" transactions. The terms "preceding" and "subsequent" as used herein in the context of the sequence of transactions refer to the order of the transactions in the sequence as defined by the transaction pointers specified in the transactions (which transaction points back to which other transaction, and so forth). They could equally be replaced with "predecessor" and "successor", or "antecedent" and "descendant", "parent" and "child", or such like. It does not necessarily imply an order in which they are created, sent to the network 106, or arrive at any given blockchain node 104. Nevertheless, a subsequent transaction (the descendent transaction or "child") which points to a preceding transaction (the antecedent transaction or "parent") will not be validated until and unless the parent transaction is validated. A child that arrives at a blockchain node 104 before its parent is considered an orphan. It may be discarded or buffered for a certain time to wait for the parent, depending on the node protocol and/or node behaviour.

One of the one or more outputs 203 of the preceding transaction Txocomprises a particular UTXO, labelled here UTX0o. Each UTXO comprises a value specifying an amount of the digital asset represented by the UTXO, and a locking script which defines a condition which must be met by an unlocking script in the input 202 of a subsequent transaction in order for the subsequent transaction to be validated, and therefore for the UTXO to be successfully redeemed. Typically the locking script locks the amount to a particular party (the beneficiary of the transaction in which it is included). I.e. the locking script defines an unlocking condition, typically comprising a condition that the unlocking script in the input of the subsequent transaction comprises the cryptographic signature of the party to whom the preceding transaction is locked.

The locking script (aka scriptPubkey) is a piece of code written in the domain specific language recognized by the node protocol. A particular example of such a language is called "Script" (capital S) which is used by the blockchain network. The locking script specifies what information is required to spend a transaction output 203, for example the requirement of Alice's signature. Unlocking scripts appear in the outputs of transactions. The unlocking script (aka scriptSig) is a piece of code written the domain specific language that provides the information required to satisfy the locking script criteria. For example, it may contain Bob's signature. Unlocking scripts appear in the input 202 of transactions.

So in the example illustrated, UTX00 in the output 203 of Txo comprises a locking script [Checksig PA] which requires a signature Sig PA of Alice in order for UTX00 to be redeemed (strictly, in order for a subsequent transaction attempting to redeem UTX00 to be valid). [Checksig PA] contains a representation (i.e. a hash) of the public key PA from a public-private key pair of Alice. The input 202 of Tx/ comprises a pointer pointing back to Tx/ (e.g. by means of its transaction ID, Tx1Do, which in embodiments is the hash of the whole transaction Txo). The input 202 of Do comprises an index identifying UTX0owithin Tx0, to identify it amongst any other possible outputs of Tx0. The input 202 of Tx/ further comprises an unlocking script <Sig PA> which comprises a cryptographic signature of Alice, created by Alice applying her private key from the key pair to a predefined portion of data (sometimes called the "message" in cryptography). The data (or "message") that needs to be signed by Alice to provide a valid signature may be defined by the locking script, or by the node protocol, or by a combination of these.

When the new transaction Tx/ arrives at a blockchain node 104, the node applies the node protocol. This comprises running the locking script and unlocking script together to check whether the unlocking script meets the condition defined in the locking script (where this condition may comprise one or more criteria). In embodiments this involves concatenating the two scripts: <Sig PA> < PA> I [Checksig PA] where "fl" represents a concatenation and "<...>" means place the data on the stack, and "[...]" is a function comprised by the locking script (in this example a stack-based language). Equivalently the scripts may be run one after the other, with a common stack, rather than concatenating the scripts. Either way, when run together, the scripts use the public key PA of Alice, as included in the locking script in the output of Txo, to authenticate that the unlocking script in the input of Tx/ contains the signature of Alice signing the expected portion of data. The expected portion of data itself (the "message") also needs to be included in order to perform this authentication. In embodiments the signed data comprises the whole of Tx/ (so a separate element does not need to be included specifying the signed portion of data in the clear, as it is already inherently present).

The details of authentication by public-private cryptography will be familiar to a person skilled in the art. Basically, if Alice has signed a message using her private key, then given Alice's public key and the message in the clear, another entity such as a node 104 is able to authenticate that the message must have been signed by Alice. Signing typically comprises hashing the message, signing the hash, and tagging this onto the message as a signature, thus enabling any holder of the public key to authenticate the signature. Note therefore that any reference herein to signing a particular piece of data or part of a transaction, or such like, can in embodiments mean signing a hash of that piece of data or part of the transaction.

If the unlocking script in Tx/ meets the one or more conditions specified in the locking script of Txo (so in the example shown, if Alice's signature is provided in Tx/ and authenticated), then the blockchain node 104 deems Tx/ valid. This means that the blockchain node 104 will add Do to the ordered pool of pending transactions 154. The blockchain node 104 will also forward the transaction Tx/to one or more other blockchain nodes 104 in the network 106, so that it will be propagated throughout the network 106. Once Tx/ has been validated and included in the blockchain 150, this defines UTX00 from Txoas spent. Note that Tx/ can only be valid if it spends an unspent transaction output 203. If it attempts to spend an output that has already been spent by another transaction 152, then Tx/will be invalid even if all the other conditions are met. Hence the blockchain node 104 also needs to check whether the referenced UTXO in the preceding transaction Txo is already spent (i.e. whether it has already formed a valid input to another valid transaction). This is one reason why it is important for the blockchain 150 to impose a defined order on the transactions 152.1n practice a given blockchain node 104 may maintain a separate database marking which UTX05 203 in which transactions 152 have been spent, but ultimately what defines whether a UTXO has been spent is whether it has already formed a valid input to another valid transaction in the blockchain 150.

If the total amount specified in all the outputs 203 of a given transaction 152 is greater than the total amount pointed to by all its inputs 202, this is another basis for invalidity in most transaction models. Therefore such transactions will not be propagated nor included in a block 151.

Note that in UTXO-based transaction models, a given UTXO needs to be spent as a whole. It cannot "leave behind" a fraction of the amount defined in the UTXO as spent while another fraction is spent. However the amount from the UTXO can be split between multiple outputs of the next transaction. E.g. the amount defined in UTX0o in Txocan be split between multiple UTX05 in Tx/. Hence if Alice does not want to give Bob all of the amount defined in UTX0o, she can use the remainder to give herself change in a second output of Tx/, or pay another party.

In practice Alice will also usually need to include a fee for the bitcoin node 104 that successfully includes her transaction 104 in a block 151. If Alice does not include such a fee, Txo may be rejected by the blockchain nodes 104, and hence although technically valid, may not be propagated and included in the blockchain 150 (the node protocol does not force blockchain nodes 104 to accept transactions 152 if they don't want). In some protocols, the transaction fee does not require its own separate output 203 (i.e. does not need a separate UTXO). Instead any difference between the total amount pointed to by the input(s) 202 and the total amount of specified in the output(s) 203 of a given transaction 152 is automatically given to the blockchain node 104 publishing the transaction. E.g. say a pointer to UTX00 is the only input to Tx/, and Tx/ has only one output UTX0/. If the amount of the digital asset specified in UTX00 is greater than the amount specified in UTX0i, then the difference may be assigned (or spent) by the node 104 that wins the proof-of-work race to create the block containing UTX01. Alternatively or additionally however, it is not necessarily excluded that a transaction fee could be specified explicitly in its own one of the UTX0s 203 of the transaction 152.

Alice and Bob's digital assets consist of the UTX0s locked to them in any transactions 152 anywhere in the blockchain 150. Hence typically, the assets of a given party 103 are scattered throughout the UTX0s of various transactions 152 throughout the blockchain 150. There is no one number stored anywhere in the blockchain 150 that defines the total balance of a given party 103. It is the role of the wallet function in the client application 105 to collate together the values of all the various UTX05 which are locked to the respective party and have not yet been spent in another onward transaction. It can do this by querying the copy of the blockchain 150 as stored at any of the bitcoin nodes 104.

Note that the script code is often represented schematically (i.e. not using the exact language). For example, one may use operation codes (opcodes) to represent a particular function. "OP_..." refers to a particular opcode of the Script language. As an example, OP_RETURN is an opcode of the Script language that when preceded by OP_FALSE at the beginning of a locking script creates an unspendable output of a transaction that can store data within the transaction, and thereby record the data immutably in the blockchain 150.

E.g. the data could comprise a document which it is desired to store in the blockchain.

Typically an input of a transaction contains a digital signature corresponding to a public key PA. In embodiments this is based on the ECDSA using the elliptic curve secp256k1. A digital signature signs a particular piece of data. In some embodiments, for a given transaction the signature will sign part of the transaction input, and some or all of the transaction outputs.

The particular parts of the outputs it signs depends on the SIGHASH flag. The SIGHASH flag is usually a 4-byte code included at the end of a signature to select which outputs are signed (and thus fixed at the time of signing).

The locking script is sometimes called "scriptPubKey" referring to the fact that it typically comprises the public key of the party to whom the respective transaction is locked. The unlocking script is sometimes called "scriptSig" referring to the fact that it typically supplies the corresponding signature. However, more generally it is not essential in all applications of a blockchain 150 that the condition for a UTXO to be redeemed comprises authenticating a signature. More generally the scripting language could be used to define any one or more conditions. Hence the more general terms "locking script" and "unlocking script" may be preferred.

3. SIDE CHANNEL As shown in Figure 1, the client application on each of Alice and Bob's computer equipment 102a, 120b, respectively, may comprise additional communication functionality. This additional functionality enables Alice 103a to establish a separate side channel 107 with Bob 103b (at the instigation of either party or a third party). The side channel 107 enables exchange of data separately from the blockchain network. Such communication is sometimes referred to as "off-chain" communication. For instance this may be used to exchange a transaction 152 between Alice and Bob without the transaction (yet) being registered onto the blockchain network 106 or making its way onto the chain 150, until one of the parties chooses to broadcast it to the network 106. Sharing a transaction in this way is sometimes referred to as sharing a "transaction template". A transaction template may lack one or more inputs and/or outputs that are required in order to form a complete transaction. Alternatively or additionally, the side channel 107 may be used to exchange any other transaction related data, such as keys, negotiated amounts or terms, data content, etc. The side channel 107 may be established via the same packet-switched network 101 as the blockchain network 106. Alternatively or additionally, the side channel 301 may be established via a different network such as a mobile cellular network, or a local area network such as a local wireless network, or even a direct wired or wireless link between Alice and Bob's devices 102a, 102b. Generally, the side channel 107 as referred to anywhere herein may comprise any one or more links via one or more networking technologies or communication media for exchanging data "off-chain", i.e. separately from the blockchain network 106. Where more than one link is used, then the bundle or collection of off-chain links as a whole may be referred to as the side channel 107. Note therefore that if it is said that Alice and Bob exchange certain pieces of information or data, or such like, over the side channel 107, then this does not necessarily imply all these pieces of data have to be send over exactly the same link or even the same type of network.

4. FINITE-STATE MACHINES A finite-state machine is defined herein as a computational model that can be implemented in hardware or software and used to simulate sequential logic and some computer programs. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The state machine can change from one state to another in response to some external inputs. The change from one state to another is called a transition. For some states, it might not be possible to have a transition to some other states.

Figure 3 illustrates an example finite-state machine 300 with two states, A and B. From each state it is possible to stay in the current state (transitions 2 and 4), or change to the other state (transitions land 3).

5. REPRESENTING A STATE MACHINE ON THE BLOCKCHAIN Figure 4 illustrates an example system 400 for representing a state machine on a blockchain 150, or put another way, for generating and implementing a blockchain-based state machine. As shown, this example system 400 includes a first party 401, a second party 402, a third party 403 and one or more nodes 104 of a blockchain network 106. Each of the first party 401, second party 402 and third party 403 may be configured to perform any or all of the actions described above as being performed by Alice 103a and/or Bob 103b. Whilst shown as being distinct parties in Figure 4, in some examples the first and second parties may be the same party. Note that the second party 402 may simply be a device, and the term "party" does not necessarily imply any user or group of users.

In embodiments, the first party 401 is configured to generate a plurality of transactions that together represent all possible states of a state machine, and supply the transactions to the second party 402. Each transaction represents a state that can be reached by the state machine. The transactions are unpublished at the time they are sent to the second party 402, meaning they have not been recorded on the blockchain 150.

Here, "all possible states" means each state that the state machine may transition to during any possible sequence of transitions, and not merely each distinct state. For example, referring to the state machine 300 shown in Figure 3, the state machine 300 has two distinct states (A and B). However, the state machine 300 may reach more than two possible states during different sequences of transitions. For instance, a first sequence of transitions may give rise to the following possible states: state A, state A, state B, whereas a second sequence of transitions may give rise to the following possible states: state A, state B, state A. Here, it is assumed that the state machine starts in state A and can go through two transitions. It will be appreciated that the number of possible states will depend on the number of distinct states, the number of states that can be reached from each state, and the number of overall transitions that the state machine may go through.

The second party 402 comprises, and/or is configured to operate, a device that is configured to implement the state machine. That is, the device is configured to start in an initial state of the state machine and transition through each possible state of the state machine. In general the device may be any type of device. For example, the device may be an loT device, a sensor, a vending machine, an elevator, a traffic light, an electronic lock (or a system comprising a lock, such as a door, car or turnstile). In some examples, the state machine may be implemented in hardware (comprised by the device) or software (run on the device), or a combination of the two.

The first party 401 may generate the plurality of transactions by first generating an initial transaction that represents an initial (i.e. starting) state of the state machine. The initial transaction may reference any previous transaction output. The initial transaction has a first output. Here, "first" is used a label for a particular output, and not necessarily the output that appears first in the list of outputs of the initial transaction. The initial transaction may comprise an indication (e.g. code) that indicates that the initial transaction represents the initial state.

Then, for each possible state that can be reached from the initial state, the first party 401 may generate a respective transaction that represents the respective possible state. For instance, if two states can be reached from the initial state, two transactions are generated, or if three states can be reached, three transactions are generated. Each transaction that is generated has an input that references the first output of the initial transaction. Each transaction has a respective first output. Like the initial transaction, each transaction may comprise an indication that that indicates that the respective transaction represents a respective state of the state machine.

This process is repeated until a transaction has been generated for each possible state that the state machine can transition to. For example, if two states may be reached from the initial state, two transactions are generated -a first transaction representing a first state and a second transaction representing a second state. Both transactions (first and second) have an input referencing the first output of the initial transaction. If two states can be reached from the first state, two more transactions are generated, both of which have an input that references the first output of the first transaction. If three states can be reached from the second state, three more transactions are generated, each of which have an input that references the first output of the second transaction.

By repeating this process, the first party 401 generates a plurality of chains of transactions, where each chain of transactions begins with the initial transaction and are connected by the output of a previous transaction in the chain being referenced by the input of a next transaction in the chain. Each chain of transactions represents a possible sequence of states through which the state machine may transition.

In some examples, the state machine may be configured to transition through a limited loop. In these examples, the number of loops is specified at the time of creating the transactions.

The plurality of transactions may be generated in alternative ways. For example, the first party 401 may generate a directed graph (i.e. tree) which represents all possible sequences of states. The graph comprises nodes (not to be confused with blockchain nodes 104) and edges. Each node represents a reachable state. Each edge represents a transition from one node to the next. The graph comprises an initial node representing an initial state, from which each other node can be traced back to. Each node may be a parent to one or more nodes. Each node may be a child of one or more nodes. The first party 401 may then generate a transaction for each node in the graph, where each transaction represents the corresponding state. Edges are represented by an input of a child transaction (representing a child node of the graph) referencing an output of a parent transaction (representing a parent node of the graph).

The first party 401 may sign each of the transactions. That is, each first output of each transaction may require the input that references the first output to comprise a digital signature corresponding to a public key. The first party 401 may generate these signatures and include them in the transactions. In some examples, each first output is locked to the same public key, and so the same private key is used to generate each signature. In other examples, one or more outputs may be locked to different public keys, in which case different private keys are used to generate the signatures. In some examples, each first output may comprise a pay-to-public-key (P2PK) or pay-to-public-key-hash (P2PKH) script.

As mentioned, each transaction may comprise an indication (i.e. a data item) that indicates (i.e. represents) the state represented by that transaction. The indication may be included in the first output of the transaction, e.g. following a return (e.g. OP_RETURN) opcode. In some examples, each transaction may have a second output that comprises the indication.

Additionally or alternatively, the transaction identifier of the transaction may be mapped to the state represented by the transaction. The mappings may be stored on-chain or off-chain. The first party 401 may send the mappings to the second party 401.

The plurality of transactions are sent to the second party 402. In some examples, the first party 401 may submit the initial transaction to the blockchain network 106. Alternatively, the second party 402 may submit the initial transaction to the blockchain network 106, e.g. signalling that the device is in the initial state.

The second party 402 is configured to (e.g. the device operated by the second party 402) submit transactions to the blockchain network 106. For example, when the device changes state from the initial state to a new state, the second party 402 submits the transaction representing the new state to the blockchain network 106. Then, when the device changes from the current state to a next state, the second party 402 submits the transaction representing the next state to the blockchain network 106. Generally, each time the device transitions to a new state, the transaction representing that state is sent to the blockchain network 106. This creates a chain of published transactions that represent the sequence of states followed by the device.

The device may be configured to change state in response to an off-chain input. That is, the inputs that cause the device to transition from one state to the next may be unrelated to the blockchain 150. For example, a device may change in response to a user input, e.g. a key card presented to a door lock, or coins deposited to a vending machine, etc. In other examples, the device may be configured to change state ion response to on-chain inputs, e.g. the presence of a particular transaction, or a transaction containing particular data, or the blockchain reaching a particular block height, etc. The third party 403 may use the published transactions to determine a current state of the device. Similarly, the third party 403 may use the chain of published transactions to determine the sequence of states taken by the device, i.e. to re-play the state machine.

6. BLOCKCHAIN-BASED STATE MACHINE This section describes further specific examples of the described embodiments. It will be appreciated that some of the features described below are optional. Moreover, any feature described below may be used in conjunction with any of the features described in the section above.

A finite-state machine may be implemented as a tree of unpublished blockchain transactions, where: * each transaction represents a state, and * a new transaction spending a transaction output represents a transition from one state to another.

A chain of transactions therefore represents an ordered sequence of states and their respective transitions. Given a state (i.e. a transaction in the tree), each reachable state is represented as a child of this transaction. Alternative states (tree branches) are implemented by having two or more transactions (attempting to) spend the same transaction outpoint. Transaction trees are pre-created and stored locally. In some examples, all of the required signatures are generated. When a transition from a state to another occurs, the transaction containing the new state is published on-chain and it becomes the new current state. Other tree branches can no longer be published as they are effectively double-spends, and they would be rejected by the blockchain network 106. Eventually, the state machine follows only one possible path through the tree, from the root to a leaf (or an intermediate node if it stops early). This path is immutably stored on-chain as a chain of transactions, allowing future audits and re-plays.

In this implementation, the entire state machine is known upfront. This means that the finite-state machine with all the states and all the different potential transitions can be mapped out in advance, knowing that in fact only one path will be followed. As an example, the finite-state machine 500 shown in Figure 5 may be converted to the equivalent blockchain-based state machine 600 shown in Figure 6. Note that in this example, state D must be duplicated (in two different transactions) in the blockchain-based state machine as it can be reached from two different states. All the transactions are stored locally (e.g., within the device running the state machine), and the sequence of reached states is published on-chain (Figure 7).

Blockchain-based state machines may be pre-created by the state machine owner, or a different party, using one or more private/public key pairs. The resulting tree of transactions is then deployed to the device that has to execute the state machine. In some examples, this device can only follow one of the pre-defined paths as it does not have access to the private keys required for creating and signing new transactions. Therefore, the device only needs a connection to the blockchain network 106 to publish the state transitions.

Given a finite-state machine with n states, an example creation process for an equivalent blockchain-based state machine is as follows: 1. For each state state staten in the finite-state machine, a unique code is chosen. This code is used in every transaction to link them to a state.

2. The finite-state machine initial state state1 is replicated as a transaction (e.g. Table 1). This transaction includes two outputs: a P2PKH output out/ and an unspendable output used to define the state (i.e., OP_RETURN states code).

3. For each possible transition from the statei (i.e., each outbound arrow in the finite-state machine) a transaction spending out/ is created (e.g. Table 2 and Table 3). Each new transaction contains at least an output representing the new state states (as an unspendable OP_RETURN states code output). It's worth noting that all the transactions created spend out/ (i.e., they are double-spends) and only one can therefore be published.

4. For each new transaction spending outi: a. If from the associated state state there are no outbound transactions, then a single change output is added to collect out/ (minus the transaction fee). This a final state, i.e. a leaf of the tree. Note that change outputs are optional.

b. Otherwise, if the associated state state, has at least 1 outbound transition: i. a P2PKH output outs is added.

H. A child transaction spending out is created for each outbound transition to a state state.

iii. Step 4. is repeated for each state, replacing out/ with out,.

The process just described requires the original state machine to have a deterministic number of steps. This means that the finite-state machine must not contain any infinite loop. In other words, it must be possible to deterministically map each potential path from the starting state to an ending state. If this is not the case, it is not possible to predetermine how many times a state (i.e., the loop) should be repeated, and one cannot preventively establish when the machine shall stop and/or enter a final state. An example implementation that allows for loops is discussed below in section 6.4. Tx/D2

Version 1 Locktime 0 In-count 1 Out-count 1 Input list Output list Outpoint Unlocking script Seq. Num. Value Locking script Tx/D1110 < SigEobj > 1000 [P2PKH Bob_2] < PKnobj > 0 OP _RETURN < state _ x > Table 1: transaction representing a state x. TxID3

Version 1 Locktime 0 In-count 1 Out-count 1 Input list Output list Outpoint Unlocking script Seq. Num. Value Locking script Tx/D2110 < 5igEob_2 > 1000-fee [P2PKH Bob 3] < PKeob 2> 0 OP RETURN < state_y >

Table 2

TxID3(bis) Version 1 Locktime 0 In-count 1 Out-count 1 Input list Output list Outpoint Unlocking script Seq. Num. Value Locking script Tx/D2110 < SigBob 2 > 1000-fee [P2PKH Bob_3] < PK13ob_2 > 0 OP _RETURN < state_z > Table 3: transactions representing two possible transitions from state x to state y or state z. Only one can be published on-chain as they both spend TxID2.

Blockchain-based state machines, in the form of trees of unpublished transactions, can be deployed at any time to the devices that will eventually execute them. The transactions are stored locally and, only when the machine is executed, the followed path is published on-chain. In some examples, each transaction is published at the same time as the state transition happens (real-time logging), otherwise their publication can be deferred (delayed logging).

An example execution of a blockchain-based state machine, already created and deployed to a device, is as follows: 1. When the blockchain-based state machine starts: I. the initial state (tree root transaction) is published on the blockchain 150. At this stage, the future possible n states are represented as tree branches that exist as private (non-published) transactions.

II. The spending options tx/, tx, are loaded, and become the possible state transitions si, sn from the current state.

2. Every time there is a state transition sx: I. the relative transaction tx is published on-chain.

II. the state is updated and sx becomes the new current state.

III. If current transaction tx is final (i.e., the blockchain-based state machine does not contain any transaction that spends it) then the blockchain-based state machine terminates.

IV. Otherwise, the new possible state transitions tx/, txm from sx are S loaded and Step 2 is repeated.

6.1 Alternative ways for representing the state In the blockchain-based state machine implementation just discussed, the states are represented using OP_RETURN. However, using OP_RETURN to store the state name (or code) is just one example, and other techniques can be adopted. For example, each transaction ID may be directly mapped to the state it represents and the relative mapping table can be stored by a trusted third-party (e.g., a web server). This approach allows for lighter transactions (as only one outpoint is required) and, ultimately, for space savings for the devices storing the transaction tree. However, lighter transactions come at expense of readability, in fact, only the state structure is stored on-chain. In order to guarantee auditability and provable re-playability, a copy of the mapping table (or its hash) may be published on the blockchain 150.

6.2 BSV state machines It's worth noting that the blockchain-based state machine implementation is general and can be applied to Bitcoin (BSV) and its forks (BTC and BCH). However, after the BSV Genesis update, OP_RETURN payloads can appear after P2PKH script patterns. Therefore there is no need to separate the output (P2PKH) and the state (OP_RETURN), making blockchain-based state machines built on BSV more efficient (i.e., smaller transaction size).

6.3 State machine verification Blockchain-based state machines can always be provably verified and replayed, as all the states and relative transitions are publicly available on-chain. Given an initial state anyone can follow the chain of transactions and verify the final state and all the intermediary states.

Similarly, given a final state, anyone can trace back the transaction history and verify all previous states, to the initial state.

If only verification of the final state is required, the techniques of UK patent application no. GB2200400.6 may be used to verify the final state by looking at the final transaction. With this technique there is no need to trace back the whole state machine transaction history to check the correctness of the final state (i.e. to check that a final state was reached by a given state machine by starting from a given initial state).

6.4 Loops A loop is defined herein as a set of one or more transitions that reach the same state. For example, Figure 8 shows two examples of state machines with loops.

Loops may be emulated using a blockchain-based state machine by a chain of transactions: each loop can be implemented by unrolling the states that compose it in a sequence of transactions repeating the same "loop pattern". Each time the loop pattern is repeated, it represents a loop cycle. This approach requires that, when the state machine is created, a cap on the maximum number of loops must be pre-determined. As an example, the blockchain-based state machine representing the state machines shown in Figure 8 are shown in Figure 9.

7. EXAMPLE USE CASES

7.1 Controllers and loT Finite-state machines describe logical processes through mathematical models. In engineering, especially in the field of controllers and loT, this approach to represent systems finds countless applications. In this context, state machines can be used to represent device states (e.g. on/off, starting, idle, error, etc). Blockchain-based state machines may be used to design next-generation controllers and loT devices whose state can be recorded immutably and transparently and audited at any time.

Using the described embodiments, a device manufacturer may create blockchain-based state machines and deploy them to the devices they are selling. These devices only need an internet connection to activate and execute (i.e., publish the relative transactions) the instructions. This type of state machine guarantees, at any time, that the execution path follows the pre-defined manufacturer logic.

As a particular example, a blockchain-based state machine may be deployed to a security system which transitions between various forms of locked and unlocked states. In such systems, the current state, previous states, and reasons for transitions between states are important. Integrating such a system with the blockchain 150 as described herein provides additional guarantee for the performance of a system.

7.2 Service Provider (Error checking) Alice is a boiler manufacturer who makes and sell boilers. Bob is a customer who has purchased one of Alice's boilers. Charlie is a separate repairperson who does not have any affiliation with the manufacturer Alice. This example can be applied to any technology that may require third party servicing (e.g. car MOT's, computer repairs, home security systems, etc.).

The boiler's that Alice manufacturers utilise a blockchain-based state machine that generates blockchain transactions containing information related to the boiler's states. This allows all interested parties (Alice, Bob, and Charlie) to provably determine the chain of events that the boiler has proceeded through.

For example, if the boiler moved to an error state, this may be automatically logged into a published transaction that Alice, Bob, and Charlie can all see on-chain. This allows Alice, the manufacturer, to use the immutable record of states and transactions for playback and debugging by going through all previous states and identifying what caused this error state.

Further, if Charlie is called out to repair the boiler, he can use the same technique to better understand the historical progression of the states to potentially solve the error state.

A benefit of such a system is that Alice and Bob can ensure that the repairperson Charlie does not carry out any unnecessary work whilst repairing the boiler. Currently systems often offer local/internal error logs, where a repairperson can over-inflate the errors to provide more services than required and thus inflate the cost. Using the distributed error log provides and immutable and transparent protocol for all parties to guarantee their shared information (e.g., the error log) and create accountability for the service provided by Charlie.

Further, once Charlie has provided his service this can also be logged using a transaction to guarantee the service provided was correct for the error state published. If a related error occurred a future instance, any of Alice or Bob could prove that Charlie made an attempt to solve the error and hold him accountable.

8. FURTHER REMARKS Other variants or use cases of the disclosed techniques may become apparent to the person skilled in the art once given the disclosure herein. The scope of the disclosure is not limited by the described embodiments but only by the accompanying claims.

For instance, some embodiments above have been described in terms of a bitcoin network 106, bitcoin blockchain 150 and bitcoin nodes 104. However it will be appreciated that the bitcoin blockchain is one particular example of a blockchain 150 and the above description may apply generally to any blockchain. That is, the present invention is in by no way limited to the bitcoin blockchain. More generally, any reference above to bitcoin network 106, bitcoin blockchain 150 and bitcoin nodes 104 may be replaced with reference to a blockchain network 106, blockchain 150 and blockchain node 104 respectively. The blockchain, blockchain network and/or blockchain nodes may share some or all of the described properties of the bitcoin blockchain 150, bitcoin network 106 and bitcoin nodes 104 as described above.

In preferred embodiments of the invention, the blockchain network 106 is the bitcoin network and bitcoin nodes 104 perform at least all of the described functions of creating, publishing, propagating and storing blocks 151 of the blockchain 150. It is not excluded that there may be other network entities (or network elements) that only perform one or some but not all of these functions. That is, a network entity may perform the function of propagating and/or storing blocks without creating and publishing blocks (recall that these entities are not considered nodes of the preferred bitcoin network 106).

In other embodiments of the invention, the blockchain network 106 may not be the bitcoin network. In these embodiments, it is not excluded that a node may perform at least one or some but not all of the functions of creating, publishing, propagating and storing blocks 151 of the blockchain 150. For instance, on those other blockchain networks a "node" may be used to refer to a network entity that is configured to create and publish blocks 151 but not store and/or propagate those blocks 151 to other nodes.

Even more generally, any reference to the term "bitcoin node" 104 above may be replaced with the term "network entity" or "network element", wherein such an entity/element is configured to perform some or all of the roles of creating, publishing, propagating and storing blocks. The functions of such a network entity/element may be implemented in hardware in the same way described above with reference to a blockchain node 104.

Some embodiments have been described in terms of the blockchain network implementing a proof-of-work consensus mechanism to secure the underlying blockchain. However proofof-work is just one type of consensus mechanism and in general embodiments may use any type of suitable consensus mechanism such as, for example, proof-of-stake, delegated proof-of-stake, proof-of-capacity, or proof-of-elapsed time. As a particular example, proofof-stake uses a randomized process to determine which blockchain node 104 is given the opportunity to produce the next block 151. The chosen node is often referred to as a validator. Blockchain nodes can lock up their tokens for a certain time in order to have the chance of becoming a validator. Generally, the node who locks the biggest stake for the longest period of time has the best chance of becoming the next validator.

It will be appreciated that the above embodiments have been described by way of example only. More generally there may be provided a method, apparatus or program in accordance

with any one or more of the following Statements.

Statement 1. A computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, and wherein the method is performed by a first party and comprises: generating a plurality of transactions representing all possible states of the state machine, said generating comprising: generating an initial transaction, wherein the initial transaction represents an initial state of the state machine and comprises a respective first output; for each respective state to which the initial state can transaction, generating a respective transaction, wherein the respective transaction represents the respective state and comprises a respective input referencing the respective first output of the initial transaction, and a respective spendable output; repeating a process of generating respective transactions representing respective states until each possible state through which the state machine can transition has been represented by a respective transaction, wherein each respective transaction comprises a respective input that references a respective first output of a previous respective transaction that represents a previous state from which the state machine can transition to reach the respective state represented by the respective transaction, and a respective first output; and sending the plurality of transactions available to a second party, wherein the second party operates a device configured to implement the state machine.

Statement 2. The method of statement 1, wherein each respective transaction is signed by the first party.

Statement 3. The method of statement 2, wherein each respective transaction is signed using a same private key.

Statement 4. The method of statement 2, wherein one, some or all of the respective transactions are signed using a different private key.

Statement 5. The method of any preceding statement, wherein each respective transaction comprises a respective data item mapped to a respective state.

Statement 6. The method of statement 5, wherein the respective first output of each respective transaction comprises the respective data item.

Statement 7. The method of statement 5, wherein each respective transaction comprises a respective second output, wherein the respective second output comprises the respective data item.

Statement 8. The method of statement 5, wherein the respective data item comprises a respective transaction identifier of the respective transaction.

Statement 9. The method of any preceding statement, wherein the state machine comprises a loop comprising a finite number of state transitions.

Statement 10. The method of any preceding statement, comprising: sending the initial transaction to one or more blockchain nodes for publishing on the blockchain.

Statement 11. The method of any preceding statement, wherein the first party is the second party.

Statement 12. A computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, wherein the method is performed by a second party, wherein the second party comprises a device configured to implement the state machine, and wherein the method comprises: receiving a plurality of transactions representing the state machine, wherein the plurality of transactions are generated by comprising: generating an initial transaction, wherein the initial transaction represents an initial state of the state machine and comprises a respective first output; for each respective state to which the initial state can transaction, generating a respective transaction, wherein the respective transaction represents the respective state and comprises a respective input referencing the respective first output of the initial transaction, and a respective spendable output; and repeating a process of generating respective transactions representing respective states until each possible state through which the state machine can transition has been represented by a respective transaction, wherein each respective transaction comprises a respective input that references a respective first output of a previous respective transaction that represents a previous state from which the state machine can transition to reach the respective state represented by the respective transaction, and a respective first output; in response to a respective transition from a respective state to a respective next state of the state machine, sending the respective transaction representing the respective next state to one or more blockchain nodes for publishing on the blockchain.

Statement 13. The method of statement 12, comprising: in response to each respective transition from a respective previous state to a respective next state of the state machine, sending the respective transaction representing the respective next state to one or more blockchain nodes for publishing on the blockchain.

Statement 14. The method of statement 12 or statement 13, wherein one or more respective transitions are caused by a respective off-chain stimulus.

Statement 15. The method of any of statements 12 to 14, wherein one or more respective transactions are caused by a respective on-chain stimulus.

Statement 16. A computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, and wherein the method is performed by a first party and comprises: generating a state graph representing a plurality of ordered sequences of states through which the state machine can transition, wherein the state graph comprises a plurality of nodes and a plurality of edges, each respective node representing a respective state and each respective edge connecting a respective previous node to a respective next node represents a respective transaction from a respective previous state to a respective next state, wherein each respective node can be traced back to an initial node representing an initial state, wherein each respective node can be a respective parent node to one or more respective child nodes, and wherein each respective child node can be a respective child node of one or more respective parent nodes; generating a plurality of transactions, wherein each transaction is mapped to a respective node of the state graph, and wherein each respective edge connecting a respective previous node to a respective next node is represented by a respective reference to a respective previous transaction mapped to the respective previous node by a respective next transaction mapped to the respective next node; and sending the plurality of transactions available to a device configured to implement the state machine.

Statement 17. A computer-implemented method of re-playing a state machine, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, wherein a blockchain comprises a chain of respective transactions, each respective transaction representing a respective state of the state machine, wherein the chain of transactions comprises an initial transaction representing an initial state of the state machine, and wherein the method is performed by a third party and comprises: obtaining each respective transaction in the chain of transactions; and determining a sequence of respective states through which the state machine has transitioned based on the respective states represented by the respective transactions in the chain of transactions.

Statement 18. Computer equipment comprising:

memory comprising one or more memory units; and processing apparatus comprising one or more processing units, wherein the memory stores code arranged to run on the processing apparatus, the code being configured so as when on the processing apparatus to perform the method of any of statements 1 to 17.

Statement 19. A computer program embodied on computer-readable storage and configured so as, when run on one or more processors, to perform the method of any of statements 1 to 17.

S

According to another aspect disclosed herein, there may be provided a method comprising the actions of the first party and the second party.

According to another aspect disclosed herein, there may be provided a system comprising the computer equipment of the first party and the second party.

Claims

CLAIMS1. A computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, and wherein the method is performed by a first party and comprises: generating a plurality of transactions representing all possible states of the state machine, said generating comprising: generating an initial transaction, wherein the initial transaction represents an initial state of the state machine and comprises a respective first output; for each respective state to which the initial state can transaction, generating a respective transaction, wherein the respective transaction represents the respective state and comprises a respective input referencing the respective first output of the initial transaction, and a respective spendable output; repeating a process of generating respective transactions representing respective states until each possible state through which the state machine can transition has been represented by a respective transaction, wherein each respective transaction comprises a respective input that references a respective first output of a previous respective transaction that represents a previous state from which the state machine can transition to reach the respective state represented by the respective transaction, and a respective first output; and sending the plurality of transactions available to a second party, wherein the second party operates a device configured to implement the state machine.
2. The method of claim 1, wherein each respective transaction is signed by the first party.
3. The method of claim 2, wherein each respective transaction is signed using a same private key.
4. The method of claim 2, wherein one, some or all of the respective transactions are signed using a different private key.
5. The method of any preceding claim, wherein each respective transaction comprises a respective data item mapped to a respective state.
6. The method of claim 5, wherein the respective first output of each respective transaction comprises the respective data item.
7. The method of claim 5, wherein each respective transaction comprises a respective second output, wherein the respective second output comprises the respective data item.
8. The method of claim 5, wherein the respective data item comprises a respective transaction identifier of the respective transaction.
9. The method of any preceding claim, wherein the state machine comprises a loop comprising a finite number of state transitions.
10. The method of any preceding claim, comprising: sending the initial transaction to one or more blockchain nodes for publishing on the blockchain.
11. The method of any preceding claim, wherein the first party is the second party.
12. A computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, wherein the method is performed by a second party, wherein the second party comprises a device configured to implement the state machine, and wherein the method comprises: receiving a plurality of transactions representing the state machine, wherein the plurality of transactions are generated by comprising: generating an initial transaction, wherein the initial transaction represents an initial state of the state machine and comprises a respective first output; for each respective state to which the initial state can transaction, generating a respective transaction, wherein the respective transaction represents the respective state and comprises a respective input referencing the respective first output of the initial transaction, and a respective spendable output; and repeating a process of generating respective transactions representing respective states until each possible state through which the state machine can transition has been represented by a respective transaction, wherein each respective transaction comprises a respective input that references a respective first output of a previous respective transaction that represents a previous state from which the state machine can transition to reach the respective state represented by the respective transaction, and a respective first output; in response to a respective transition from a respective state to a respective next state of the state machine, sending the respective transaction representing the respective next state to one or more blockchain nodes for publishing on the blockchain.
13. The method of claim 12, comprising: in response to each respective transition from a respective previous state to a respective next state of the state machine, sending the respective transaction representing the respective next state to one or more blockchain nodes for publishing on the blockchain.
14. The method of claim 12 or claim 13, wherein one or more respective transitions are caused by a respective off-chain stimulus.
15. The method of any of claims 12 to 14, wherein one or more respective transactions are caused by a respective on-chain stimulus.
16. A computer-implemented method for representing a state machine using a blockchain, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, and wherein the method is performed by a first party and comprises: generating a state graph representing a plurality of ordered sequences of states through which the state machine can transition, wherein the state graph comprises a plurality of nodes and a plurality of edges, each respective node representing a respective state and each respective edge connecting a respective previous node to a respective next node represents a respective transaction from a respective previous state to a respective next state, wherein each respective node can be traced back to an initial node representing an initial state, wherein each respective node can be a respective parent node to one or more respective child nodes, and wherein each respective child node can be a respective child node of one or more respective parent nodes; generating a plurality of transactions, wherein each transaction is mapped to a respective node of the state graph, and wherein each respective edge connecting a respective previous node to a respective next node is represented by a respective reference to a respective previous transaction mapped to the respective previous node by a respective next transaction mapped to the respective next node; and sending the plurality of transactions available to a device configured to implement the state machine.
17. A computer-implemented method of re-playing a state machine, wherein the state machine comprises a plurality of respective states, wherein each respective state can transition to one or more respective states, wherein a blockchain comprises a chain of respective transactions, each respective transaction representing a respective state of the state machine, wherein the chain of transactions comprises an initial transaction representing an initial state of the state machine, and wherein the method is performed by a third party and comprises: obtaining each respective transaction in the chain of transactions; and determining a sequence of respective states through which the state machine has transitioned based on the respective states represented by the respective transactions in the chain of transactions.
18. Computer equipment comprising: memory comprising one or more memory units; and processing apparatus comprising one or more processing units, wherein the memory stores code arranged to run on the processing apparatus, the code being configured so as when on the processing apparatus to perform the method of any of claims 1 to 17.
19. A computer program embodied on computer-readable storage and configured so as, when run on one or more processors, to perform the method of any of claims 1 to 17.