Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03K—PULSE TECHNIQUE
  • H03K19/00—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits
  • H03K19/02—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components
  • H03K19/173—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components
  • H03K19/177—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components arranged in matrix form
  • H03K19/17704—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components arranged in matrix form the logic functions being realised by the interconnection of rows and columns
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/20—Design optimisation, verification or simulation
  • G06F30/22—Design optimisation, verification or simulation using Petri net models
• • G—PHYSICS
  • G11—INFORMATION STORAGE
  • G11C—STATIC STORES
  • G11C29/00—Checking stores for correct operation ; Subsequent repair; Testing stores during standby or offline operation
  • G11C29/006—Checking stores for correct operation ; Subsequent repair; Testing stores during standby or offline operation at wafer scale level, i.e. wafer scale integration [WSI]
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03K—PULSE TECHNIQUE
  • H03K19/00—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits
  • H03K19/02—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components
  • H03K19/173—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components
  • H03K19/177—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components arranged in matrix form
  • H03K19/17724—Structural details of logic blocks
  • H03K19/17728—Reconfigurable logic blocks, e.g. lookup tables
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03K—PULSE TECHNIQUE
  • H03K19/00—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits
  • H03K19/02—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components
  • H03K19/173—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components
  • H03K19/177—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components arranged in matrix form
  • H03K19/17736—Structural details of routing resources
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03K—PULSE TECHNIQUE
  • H03K19/00—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits
  • H03K19/02—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components
  • H03K19/173—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components
  • H03K19/177—Logic circuits, i.e. having at least two inputs acting on one output; Inverting circuits using specified components using elementary logic circuits as components arranged in matrix form
  • H03K19/17736—Structural details of routing resources
  • H03K19/1774—Structural details of routing resources for global signals, e.g. clock, reset

Definitions

• aspects of this invention pertain to several interrelated fields. These fields include digital logic circuits, programmable and reprogrammable logic devices, the architecture of computing « structures, and computer-aided design systems. More particularly, the invention involves a reprogrammable, asynchronous logic cell which, may be configured in an arbitrarily large two-dimensional (or three-dimensional) array of such cells to perform virtually any logic operation. The invention is particularly well-suited to the implementation of logic circuits and systems that can be characterized as a class of Petri Nets.
• Concurrent systems are important in, among other areas, logic design and computer architecture. In those areas, concurrent systems are viewed as useful for providing more processing power and speed than can a conventional single processor or sequential logic system.
• CHiP Configurable, Highly Parallel
• Poker Parallel Programming Environment
• microprocessor or the like, as the kernel of processing power.
• microprocessors may not provide an adequate solution to a problem; even relatively simple tasks may require so many instruction cycles to accomplish that the effective speed of the microprocessor may not be sufficient.
• Petri Net is a formal model for concurrent systems. Petri Nets may be used to model a wide range of systems, and can represent arbitrarily complex behavior.
• the mathematical definition of a Petri Net is well-known and can be found in any of a number of references.
• T. Agerwala "Putting Petri Nets to Work," IEEE Computer, December 1979/ at * 85-94, which is hereby incorporated by reference for its discussion of Petri Nets.
• T denotes a set of "transitions” (or “events")
• P is a set of "places” (or “states”)
• A is a set of directed arcs from transitions to places and vice versa.
• the union of transitions and places defines the "nodes” of the system.
• “Tokens” may be assigned to places in the net. A transition is said to be “enabled” in a Petri Net if each of its input places has a token.
• An enabled transition can "fire” by removing a token from each of its input places and putting a token in each of its output places. Tokens are indivisible; that is, a token can be removed from a place by only one transition. In general, the firing of transitions proceeds asynchronously.
• Concurrency means that transitions are relatively independent; that is, the firing of a pair of transitions can occur in an arbitrary order if both transitions are enabled and the transitions do not share input places.
• Conscurrt occurs when two transitions that share an input place are enabled at the same time, such that the firing of one cf those transitions disables the other. . *
• Th ' e transitions, places and tokens of a Petri Net are readily mapped to the variables occurring in physical systems.
• a net could represent a manufacturing plant, with input places representing materials reaching work stations, transitions representing processing taking place at the work station, output places representing the results of the work station's operation and tokens representing the quanta of material required to reach a work station before it can perform its processing.
• Digital systems both synchronous and asychronous are also readily representable using Petri Nets.
• Petri Nets for system modelling makes available a variety of techniques for system synthesis and analysis.
• Petri Nets in computer circuitry i.e., digital logic
• circuitry i.e., digital logic
• Petri Nets capable of embodying all or nearly all types of Petri Nets.
• circuit modules are substituted directly for transitions and places.
• Another approach has been to provide a basic collection of Petri Net functions and corresponding speed-independent hardware * blocks. Complete circuits are assembled directly • from these blocks.
• a transistor-level implementation has also been described in the literature for various circuits which can be combined to create realizations for Petri Nets of different types. See E.
• Patil and T.A. Welch "A Programmable Logic Approach for VLSI,” IEEE Transactions on Computers, Vol. C-28, No. 9, September 1979, at 594-601.
• the Patil and Welch structure is a form of programmable logic array which provides conventional AND and OR functions, while also containing flip-flops distributed throughout the array. It allows portions of the array to be used for independent tasks and can be operated in synchronous or asynchronous modes. However, there are restrictions on the segmentation of areas of the array inasmuch as control is row and column oriented. Columns may be divided into independent column segments at points provided, typically, every eight rows; while rows may be divided into independent row segments at breakpoints provided, typically, every four columns.
• Every column segment must contain at least one flip-flop.
• Each logical column can either act as a stored binary variable, or it can perform the logical OR function of the row inputs. When the column segment represents a stored variable, the values can be set and reset by the rows.
• Each row is an implicant or conjunction term over the selected column variables; a column input may be either the column value, its complement or there may be no connection from the column to that row. These variables are ANDed to form the row value.
• an object of the present invention to provide a computational apparatus and architecture in which concurrency can be extended to a much lower level than has generally been heretofore achieved.
• Still another object of the invention is a universal'digital logic circuit which can be employed to implement a large class of logic operations.
• Yet another object of the invention is to provide a reprogrammable digital logic device which can be programmed and reprogrammed easily to implement a large class of logic operations.
• Another object of the invention is to provide a reprogrammable digital logic device which can be programmed and reprogrammed easily to realize a large class of Petri Nets.
• Still another object is to provide a reprogrammable digital logic cell which can be connected to other such cells to form an array of
• a further objects of the invention is to provide such an array wherein the cells operate asynchronously, for implementation of speed- independent logic.
• Another object of the invention is to provide a method and an environment to facilitate the programming of the reprogrammable logic device and systems employing the reprogrammable logic device.
• a still further object of the invention ⁇ is to provide reprogrammable logic and a user-friendly programming environment therefor, to reduce the time required for the development of a large class of digital systems.
• Yet another object of the invention is to allow a manufacturer or system developer to.work with a reduced parts inventory for digital logic, by providing a reprogrammable logic element which is usable for implementing a large class of digital functions.
• a novel asynchronous logic cell an array formed of such cells and a graphical method for programming the cells and the array.
• Each cell comprises a number of exclusive-OR gates, Muller C-elements and programmable switches.
• the array can be
• an array of chips will sometimes be referred to as a "matrix” , to distinguish such an array from an array of ce.lls internal to a chip.
• a ma.trix or portion of a matrix
• computing power can be increased by simply adding more chips to the matrix.
• the basic logic cell is reprogrammable and may even be reprogrammed dynamically, such as to perform recursive operations or simply to make use of hardware which is temporarily idle. Programming is accomplished by setting the states of the switches in each cell.
• the invention provides a general purpose architecture for computation and digital systems.
• the individual logic cells may be programmed and connected together to implement any circuit capable
• any microprocessor can be simulated in an array of such cells. Any of a number of microprocessors could be emulated, the choice being determined by the switch settings in the array. Further, the array is regular and switch settings can produce "logical wires", crossovers, connections, and routings (including right-angle bends and fan-outs) running both horizontally and vertically; consequently, it is generally possible to "wire around” defective elements. Due to this latter characteristic, the invention shows promise for so-called "wafer-scale” integration or fabrication. If a large wafer contains a few defective cells,
• those cells can simply be avoided and bypassed, with the remainder of the wafer remaining useful. This may permit the fabrication of much larger chips than has heretofore been possible, since defects normally render a chip useless.
• a first apparatus aspect of the invention is a digital logic cell characterized by: a set of logic elements comprising disjunctive and conjunctive elements, each of the disjunctive and conjunctive elements having a first input, a second input and an output; and a set of switches for programmably, operatively interconnecting the disjunctive and conjunctive elements neighboring each switch, each switch having (1) first and second signal inputs for connection to outputs of selected ones of the disjunctive and conjunctive elements and (2) at least one output for connection to an input of a selected one of the disjunctive and conjunctive elements.
• a second apparatus aspect of the invention is a digital logic cell characterized by: a set of exclusive-OR gates, each having at least two inputs and an output; a set of C-elements, each having at least two inputs and an output; a set of programmable switch assemblies having first, second, third and fourth signal leads, a
• each of such switch assemblies comprising first and second single-pole, four-throw switches,
• each exclusive-OR gate being connected to one of the first and second signal leads of first and second switch assemblies and each input of each exclusive-OR gate being connected to one of the third and fourth signal leads of each of two other switch assemblies; and the output of each C-element being connected to one of the first and second signal leads of third
• each input of each C-element being connected to one of the third and fourth signal leads of each of two other switch assemblies.
• a third apparatus aspect of the invention is a homogeneous array of digital logic cells, characterized by each cell comprising (a) a set of exclusive-OR elements, each having two inputs and an output; (b) a set of C-elements, each having two inputs and an output; and (c) a set of progammable switches selectively operable to operatively interconnect J:he exlcusive-OR elements and C-elements within a cell and to operatively interconnect the elements on the boundaries of a cell with the elements of neighboring cells.
• a first method aspect of the invention is a method of generating programming instructions for configuring an array of programmable logic cells which comprise logic elements and programmable switch assemblies, each of such switch assemblies including at least one switch having at least one signal input lead and at least one signal output lead; such method characterized by, on a work station having a display screen, input means, and a programmed processor for generating on the display screen displays of symbols representing logic elements, switch assemblies, and their connections and for processing input from the input means, the steps of:
• a template representing an unprogrammed array of switches providing on the display screen a template representing an unprogrammed array of switches; and generating a programming instruction in response to signals from the input means, such signals representing (i) selection of an output lead of a switch and (ii) selection of a source from among (a) an input led of the switch, (b) a logical one signal and (c) a logical zero signal; such programming instruction being usable by the array of cells to configure said switch assembly to connect the selected output lead to the selected source.
• a second methpd aspect of the invention is a method of generating programming instructions for configuring an array of programmable logic cells comprising logic elements and programmable switch assemblies; each programmable switch assembly having first and second signal input leads, first and second signal output leads, a zero input for connection to a logical zero source and a one input for connection to a logical zero source and a one input for connection to a logical one source; each of the switch assembly signal input leads and signal output leads being termed a "signal lead"; such method being characterized by, on a work station having a display screen, input means, and a programmed processor for generating displays for the display screen and for processing input from the input means, the steps of: providing on the display screen a template representing an unprogrammed array of cells; and
• Figs. 1A - IF are illustrations of a set of novel circuit symbols used herein to represent the elements of the present invention, and the corresponding conventional symbols used for such elements;
• Fig. 2 is a diagrammatic illustration of a portion of the medium
• Fig. 3 is a diagrammatic illustration of a single logic cell according to the invention, including some elements which are shared with neighboring cells when the cell is embedded in an array;
• Fig. 4 is an illustration of an exemplary work station display of a template for use in programming the medium of Fig. 2;
• Fig. 5 is an illustration of an exemplary program, in hexadecimal notation, for the switch settings for an area of two-by-three cells, for generating a typical circuit;
• Fig. 6 is a partially diagrammatic, partially schematic illustration showing the circuit generated by the program of Fig. 5, overlaid on the template of Fig. 4;
• Fig. 7 is a partially diagrammatic, partially schematic illustration of the circuit of Fig. 6, freed from the template; " ,
• Fig. 8 is a diagrammatic illustration of a portion of the medium with C-elements excised, showing the existence of horizontal and vertical "channels; "
• Fig. 9 is a diagrammatic illustration of a template of the medium showing the creation of logical "wires" in the horizontal direction;
• Fig. 10 is a diagrammatic illustration of a template of the medium showing the creation of logical "wires" in the vertical direction;
• Fig. 11 is a diagrammatic illustration of a template of the medium showing the creation of logical "wires" with right-angle bends;
• Fig. 12 is a diagrammatic illustration of a template of the medium showing the creation of additional logical "wires" with right-angle bends;
• Fig. 13 is a diagrammatic illustration of a template of the medium showing the creation of
• Fig. 14 is a diagrammatic illustration of a representative Petri Net
• Fig. 15A is a diagrammatic illustration of an enabled transition having two input places and two output places;
• Fig. 15B is a diagrammatic illustration of the transition and places of Fig. 15A after the transition has fired;
• Fig. 16 is a diagrammatic illustration of a shared input place in a Petri Net (i.e., a place that, is an input place to multiple transitions);
• Fig. 17A is an illustration of the diagrammatic symbol used to represent, in a Petri Net, an unshared place of arbitrary fan-in when the place has no token in the initial marking of the net;
• Fig. 17B is an illustration of the schematic circuit symbol for an exclusive-OR gate in the present invention, for implementing the place of Fig. 17A;
• Fig. 18A is an illustration of the diagrammatic symbol used to represent, in a Petri Net, an unshared place of arbitrary fan-in, when the place has a token in the initial marking of the net;
• Figs. 18B and 18C are schematic circuit diagrams for equivalent alternative implementations of the place of Fig. 18A;
• Fig. 19A is an illustration of the diagrammatic symbol used to represent a shared place in a Petri Net, when the place has no token in the initial marking of the net;
• Fig. 19B is an illustration of the schematic circuit for an implementation of the shared place of Fig. 19A;
• Fig. 20A is an illustration of the diagrammatic symbol used to represent a shared place in a Petri Net, when the place has a token in the initial marking of the net-; . •
• Figs. 20B and 20C are schematic circuit diagrams for alternative implementations of the shared place of Fig. 20A;
• Fig. 21A is an illustration of the diagrammatic symbol used to represent, in a Petri Net, a transition with no shared input places;
• Fig. 21B is an illustration of the schematic circuit for a C-element used for implementing the transition of Fig. 21A;
• Fig. 22A is an illustration of the diagrammatic symbol used to represent, in a Petri Net, a transition with two shared input places and arbitrary fan-out;
• Fig. 22B is an illustration of the schematic circuit for an implementation of the transition of Fig. 22A, according to the invention.
• Fig. 23A is an illustration of the diagrammatic symbol used to represent, in a Petri Net, a transition with an arbitrary number of
• Fig. 23B is an illustration of the schematic circuit for an implementation of the transition of Fig. 23A, according to the invention.
• Fig. 24A is an illustration of a symbol for a three-input exclusive-OR gate
• Fig. 24B is a schematic diagram of a circuit for assembling the three-input exclusive-OR gate of Fig. 24A from a pair of cascaded two-input exclusive-OR gates; • - •
• Fig. 24C is an illustration of a symbol for a three-input C-element
• Fig. 24D is a schematic diagram of a circuit for assembling the three-input C-element of Fig. 19D from a pair of cascaded two-input C-elements;
• Fig. 25A is a diagrammatic illustration of a Petri Net representation for a single stage of a bit pipeline
• Fig. 25B is a schematic diagram for a circuit implementation of the Petri Net of Fig. 25A;
• Fig. 25C is a schematic diagram for a circuit implementation equivalent to that shown in Fig. 25B, with the placement of the inverter altered to take into account the geometry of the array, laid out as it can be implemented on the medium of the invention;
• Fig. 25D is a listing of a program for setting the switches to produce the circuit of Fig. 25C, with the relative positions of the program's hexadecimal instructions corresponding to the
• Fig. 25E is a diagrammatic symbol for a block representation of the circuit of Fig. 25C.
• Each logic cell comprises a number of elements used exclusively within that cell, as well as a number of elements shared by that cell and adjacent cells, to the extent there are adjacent cells.
• a ' cell has nine exclusive-OR (“XOR") gates, four Muller C-elements ("C-elements”) and twelve programmable switches .
• XOR exclusive-OR
• C-elements Muller C-elements
• programmable switches When embedded in a two-dimensional array, however, each of the XOR gates and programmable switches on the faces of a cell is shared with another cell, and each of the C-elements (which are at the corners of the cell) is shared with three other cells.
• the plain, unfilled circle 12 in Fig. 1A represents an exclusive-OR gate whose conventional symbol is shown at 14; an alternate, equivalent symbol 13 is used in a context described below.
• a double output connection may, for convenience, be shown as at symbols 12' and 13' in Fig. IB.
• the exclusive-OR gates are used in three ways: as disjunctive elements, as "wires”, and as inverters. To see how the exclusive-OR gate functions as a disjunctive element, notice * that* whenever there is a transition (from 0 to 1 or from 1 to 0), on either input, there is a subsequent transition on the output.
• the exclusive-OR gate therefore, acts as a "merge” for transitions.
• the effect of a "wire” is achieved by setting to zero one of the two inputs of an exclusive-OR gate, as a result of which the gate's logical output level corresponds to the logic level at its other input. Because this is not a physical wire, per se, it is referred to herein as a "logical" wire.
• Anexclusive-OR gate is turned into an inverter by setting one of its inputs to one; the value of the output is then the negation of the value on the other input.
• the symbol for an inverter is shown in Fig. IC at 16, together with the conventional symbol 18.
• the second element of the cell, the C-element is illustrated in Fig. ID by the symbol 20.
• Fig. ID The second element of the cell, the C-element is illustrated in Fig. ID by the symbol 20.
• a variety of other symbols have been used in the past for this
• the C-element (the "C” stands for consensus) is a conjunctive device and is also called a "rendezvous", “join”, or “last of” circuit. It is described in the literature, such as in C.Mead and L,Conway, Introduction to VLSI Systems, Addison-Wesley Publishing Co., Reading, Massachusetts, 1980, at 254-255, and a suitable circuit is shown there.
• the C-element is a bistable device with an arbitrary number of inputs and a single output. The output provides the consensus of the inputs.
• the present cell uses only two-input C-elements.
• a two-input C-element is logically equivalent to a 3-input majority voting circuit (i.e., a 2 out of 3 circuit) which has its output
• the programmable switches provide the capability of programming the cells and the array for different tasks by changing interconnections.
• Each switch is represented as in symbol 30.
• Each switch 30 has two input wires 31X and 31Y and two output wires 31Z(1) and 31Z(2). There are also four conductors (assuming parallel operation) for controlling the state of the switch, but they are not shown in the drawing symbol.
• the switch 30 (more accurately termed a switch assembly) is the equivalent of the pair of single-pole, four-throw switches (or multiplexer) 32, which are controlled by four bits S0-S3 to provide the switching arrangement now described.
• Each of the two outputs 31Z(l)and 31Z(2) of switch 30 can be programmed in four different ways: (1) to connect to a first input, such as 3IX; (2) to connect to a second input, such as 31Y; (3) to be set to zero; or (4) to be set to one.
• Switches are, according to a convention established at this point, always depicted with one input and one output aligned horizontally and with the other input and the other output aligned vertically. This allows adoption of the following convention for the meaning of the four bits S0-S3 used to program the switches:
• the "X" symbol in a column means that the value of the bit identified at the head of that column does not enter into the decoding shown in the right hand column. That is, the first two bits SO, SI, and the last two bits S2, S3 are interpreted independently.
• 1101 (hexadecimal "D") means that the horizontal output is set to 1 and the vertical output is connected to the vertical input.
• the Array (or, as it is also called, the "computational medium") is a uniform matrix of exclusive-OR gates, C-elements and programmable switches. As exemplified herein, the matrix is
• the array may be of arbitrary size; and its boundary, of arbitrary shape.
• the present illustration is limited, however, for simplicity, to arrays or portions of arrays containing integral numbers of cells.
• a representative portion of such an array (containing nine cells) is shown at 40 in Fig. 2.
• the standard cell 42 is depicted in Fig. 3. Since a single cell is shown divorced from the array, it contains nine XOR gates 12', four C-elements 20', and twelve programmable switches 30.
• Programs for the computational medrum consist of arrays of bits: four for each programmable switch. These bits act to program a circuit in the medium, and transform the general-purpose environment of the medium into a special-purpose device.
• a work station is employed for accomplishing the programming of the medium.
• the work station is equipped with a number of "tools" to assist the programmer.
• the tools take the form of special programs and displays to facilitate the visualization of the transformation of the medium from a "blank template" to a special-purpose piece of hardware.
• a blank template corresponds to a medium in which the outputs of all switches are set to zero.
• the work station itself may be a personal
• the user calls a display screen which serves as a background template depicting the unprogrammed medium.
• the template may be displayed as a dimmed copy of the medium of Fig. 2 or it may be a different color or possess some other attribute to show that it is only a background to assist the designer.
• a switch may be set by moving the mouse to select a switch output first and to then select an input to the switch (or vice versa); this sequence is interpreted as requiring the output and input to be connected, and a corresponding switch-setting to be generated.
• the input and output connections are emphasized (e.g., darkened, solidified, or shown in another color).
• an exclusive-OR gate's input may be selected and set to zero or to one to create a logical wire or an inverter, respectively.
• the gate may be transformed to the symbol for an inverter or to a simple wire symbol.
• the numeral 50 identifies a section of the medium represented in a template form. To identify the fact that this is just a template (i.e., an unprogrammed portion of the medium) and to distinguish it from a programmed area of the medium, all lines in the template section 50 are dashed instead of solid and the alternative symbols 13 and 24 are used for the XOR gates and C-elements, instead of the symbols 12 and 20.
• Fig. 5 shows a program 55, in hexadecimal notation, for generating a circuit by programming that area.
• the spacing of the hexadecimal digits corresponds to the spacing of the switches in Fig/ 4.
• Each of the hexadecimal digits in the program of Fig. 5 represents the setting of a particular switch in a corresponding location in Fig. 4, according to the assignments of bits S0-S3 set out above.
• a switch is updated using the "mouse", for example, a hexadecimal digit is generated corresponding to the new switch setting. Using this hexadecimal digit, the work station appropriately modifies the display to show the circuit so indicated.
• Fig. 6 shows the circuit 60 generated by the program 55 of Fig. 5, overlaid on the template 50.
• the circuit has one inverter 62, two C-elements 64 and 66, and three exclusive-OR gates 68, 70 and 72.
• Various switch settings convert selected switches and exclusive-OR gates into logical (but, of course, not physical) wires; some of the wire segments are straight horizontal or vertical runs, while others involve bends or fan-outs.
• the circuit of Fig. 6 is displayed at 75 in Fig. 7, freed from the template.
• An exemplary program has been developed for programming the. medium with the aid of a personal computer.
• This program uses a "mouse”, or the like, for moving an on-screen pointer (or cursor) to a réelle "wire” (i.e., an input or an output of a switch, XOR gate, or C-element) which is to be acted upon ⁇ .
• a "mouse” i.e., an input or an output of a switch, XOR gate, or C-element
• buttons may be employed for specifying the action to be taken. These buttons are denominated the "select” button and the "option” button, respectively. They may be on the mouse, on the work station keyboard, or elsewhere.
• the wire thereby indicated is made to blink off and on, to verify its selection.
• the pointer When the pointer is moved and a second wire is selected, it may or may not be a wire that can be connected with the first wire. (The only way switches are set is by connecting inputs and outputs, or by setting wires to one or zero.) If the second wire can be connected to the first wire, the connection is made; otherwise, the first wire is de-selected and the second wire takes its place as the selected wire.
• the option button has not been used. If the option button is depressed when the select button is pressed (to designate a wire), then one of the following actions occurs: If the designated wire is connected through a switch to another wire(s), then the connection(s) is (are) broken. If the designated wire is an output of a switch that is not connected through that switch to another wire, the logical value of that wire is inverted.
• the work station' program for drawing circuits preferably obeys the following rules: When a switch output is connected to one of its'inputs, the input and output wires-of the switch are highlighted (e.g., drawn as solid lines) and a solid connection is made within the switch.
• An exclusive-OR gate is highlighted (i.e., shown as an exclusive-OR gate with a solid outline symbol 12') if both of its input wires have been highlighted; that is, if both of its inputs are connected to other elements rather than being set to zero or one.
• An exclusive-OR gate is depicted as an inverter, symbol 16, if one of its inputs is set to logical one.
• a C-element is highlighted (i.e., shown as a C-element with a solid border, using symbol 20) if either of its input wires is highlighted or set to one.
• the array structure 40 of Fig. 2 possesses some interesting and important properties.
• the C-elements have been excised to show how the exclusive-OR gates and switches form bi-directional horizontal "channels" 80 - 82 and vertical "channels" 83 - 85.
• the existence of these channels facilitates the creation of wires running horizontally (as at 92 and 94 in Fig. .9) and vertically (as at 102 and 104 in Fig. 10) across the medium or portions thereof.
• various kinds of ninety-degree bends can be created, as shown in Figs. 11 and 12 at 106-120. Equally as important, vertical crossovers and horizontal crossovers can be established, as represented at 122-128 in Fig. ' 13.
• Fig. 14 which depicts a representative Petri Net 200
• the circles 202i represent places
• the rectangular boxes 204j represent transitions
• the small black dots 206k represent tokens.
• a place may be identified as an input place of a transition or as an output place of a transition. Pictorially, this is illustrated in Figs. 15A and 15B; there, places 202a and 202b are input places to transition 204t, while places 202c and 202d are output places to transition 204t.
• the graphical representation of the firing of transitions also may be observed in
• FIGs. 15A and 15B each of input places 202a and 202b contains a token. Transition 204t is thus enabled to fire. Once that transition fires, the condition of the Petri Net is as shown in Fig. 15B. That is, a token has been taken from each of places 202a and 202b and a token has been placed in each of places 202c and 202d.
• Fig. 16 portrays a shared input place. That is, place 202f is shared by transitions 204u and 204v.
• the class of Petri Nets which can be implemented using the present invention are those Petri Nets wherein: (1) the net is "safe”, (2) the, net is “persistent”, (3) each transition has no more than two shared input places, and (4) any transition with two shared input places has no other input places.
• Petri Nets wherein: (1) the net is "safe”, (2) the, net is “persistent”, (3) each transition has no more than two shared input places, and (4) any transition with two shared input places has no other input places.
• Petri Nets electrically requires the establishment of a correspondence between tokens and electrical signals.
• the components produce transitions from logical zero to logical one and from logical one to logical zero.
• Suggested Petri Net implementations have interpreted these electrical transitions in two different ways. These two ways have been called “simple signalling” and “reset signalling”. See E. Pacas-Skewes, "A Design Methodology for Digital Systems Using Petri Nets," PhD diss., Univ. of Texas at Austin, 1979. In simple signalling, a transition of level (either 0 to 1 or 1 to 0) is identified with a token.
• Figs. 17A, 17B - 23A, 23B depict, pictorially, the correspondences between various Petri Net components and their circuit realizations according to the invention.
• the series of dots 223 represent arbitrary fan-in.
• An unshared place 220 of arbitrary fan-in, as in Fig. 17A, is implemented by an XOR gate 222 with equivalent fan-in, as in Fig. 17B.
• the unshared place in an initial marking
• the unshared place has a token, as at 224 in Fig. 18A, it is implemented with an XOR gate 226 and an
• inverter 228 arranged in one of two equivalent forms, shown in Figs. 18B and 18C, respectively, at 229A and 229B.
• the realization for a shared n-input place with a token, element 240 in Fig. 20A, may take one of two equivalent forms, as shown in Figs.” 20B and 20C, respectively, at 242A and 242B.
• the Petri Net symbol for a transition with as arbitrary number of unshared input places and arbitrary fan-out is shown at 250 in Fig. 21A; it is realized by a corresponding C-element of arbitrary fan-in and fan-out, as shown at 252 in Fig. 21B.
• the Petri Net symbol for a transition with two shared input places and arbitrary fan-out is shown at 260 in Fig. 22A, its realization is shown at 262 in Fig, 22B; the realization comprises a two-input C-element whose output feeds back to the input places as well as forward to the next stage.
• a hybrid of Figs. 21A and 22A is shown in Fig.
• FIG. 23A which depicts a Petri Net symbol for a transition 264 with one shared input state, an arbitrary number of unshared input states and arbitrary fan-out.
• the realization of the transition 264 can be accomplished with the circuit 266 of Fig. 23B, comprising a C-element of arbitrary fan-in cascaded with a two-input C-element.
• the two-input exclusive-OR gate and C-element shown in Figs. 1A - IE can be cascaded.
• the three-input exclusive-OR gate 230A of Fig. 24A can be implemented using a pair of cascaded two-input exclusive-OR gates 230B and 230C, connected as shown in Fig. 24B.
• the three-input C-element 230E of Fig. 24C can be realized from a pair of cascaded two-input C-elements 230F and 230G, connected as shown in Fig. 23D.
• Figs. 25A-25E show, for a simple example, the progression from a Petri Net 300 in Fig. 25A to a corresponding circuit 302 (Fig. 25B) to an implementation of the circuit 304 as it might be laid out in an array of cells in the computational "medium” of the invention. Only the elements used to implement the circuit are shown in Fig. 25C, of course.
• the circuit of Fig. 25C is be produced by the program 306 shown in Fig. 25D. And once the program has been generated, the circuit (in the form of the program) can be stored as a "block" for subsequent recall and reuse. In that form, it can also be displayed on the work station screen as a block, such as block 308 in Fig. 25E.
• the invention thus provides a general purpose hardware medium, much like a high-level programming language provides a general purpose programming environment.
• the invention thus provides an array structure containing but three types of elements: a single type of conjunctive element, a single type of disjunctive element and a single type of switch for
• the resulting array permits an extremely high degree of concurrent operation, since cells may operate largely independently of one another. It is even possible that different parts of the array structure may not interact with each other.
• Muller C-elements are used as the conjunctive elements and exclusive-OR gates are used as the disjunctive elements, but it may be possible to replace these particular circuit types with other conjunctive and disjunctive elements.
• tokens may be identified with manifestations or effects other than logic-level transitions. For example, tokens might be identified with an electrical effect such as charge (if charge-coupled devices are employed) , with a magnetic eff ct such as magnetic domains (if magnetic bubbles are used) or with optical or fluidic effects.
• the switches then become, broadly speaking, means for routing the selected effects or manifestations between and among the disjunctive and conjunctive elements.
• the array may be considered a bipartite structure having as two types of nodes: the switches, on the one hand, and the conjunctive/ disjunctive elements on the other hand.
• the programming environment for the array frees the hardware designer from the need to be a programmer also. That is, the designer builds a circuit in the medium by simply pointing on a work station screen to switch inputs and outputs and
• the medium is readily reprogrammed, since all that is required is to feed it new switch settings .
• circuitry for t.he switches and one or more types of the other elements might be merged.
• other topologies might be employed, such as extending the array or portions of the array into three dimensions.
• element fan-in and/or fan-out might be changed, e.g., from two to " three.
• Reset signalling might be employed, instead of only simple signalling.
• the array or portions of the array could be rotated or reflected to orientations other than that shown in the drawing.

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