JPH10228490A - Method for resolving logic function in lsi design - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide the resolving method of a logic function in LSI design, which detects the symmetry of a variable in the function, enumerates a bound set that has high possibility for giving resolution and which efficiently and economically resolves the logic function. SOLUTION: A symmetry detection part 1 detects the symmetry of the variable and obtains the set of the symmetric variables. When the set of the symmetric variables exists, an XOR resolution part 2 executes resolution by using an OR gate when symmetry is given. When a single variable symmetry is given, an AND resolution part 3 executes resolution by using the AND gate and the set except the set of the symmetric variables is not made to be the candidate of the bound set. Thus, processing time is shortened.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention can be applied to, for example, the design and optimization of a combinational logic circuit in a logic design support system, and can be applied to a logic in an LSI design for decomposing a given logic function into two logic gates having a small number of inputs. Regarding the function decomposition method, for example, the four-input logical function f shown in FIG.
The present invention relates to a method for decomposing a logic function into two logic gates consisting of an input function h and a 3-input function g.

[0002]

2. Description of the Related Art A fully specified logical function of multiple inputs and one output (hereinafter simply referred to as a function) is a variable x having a value of 0 or 1.
_i (1 ≦ i ≦ n) a mapping {0,
1｝ ⁿ → {0, 1}. Function _{f (x 1, ..., x} n)
Simple disjuncti decomposition of
ve decomposition) has the following form as shown in FIG.

F = g (h (X ^B ), X ^F ) (1) Here, X ^B and X ^F are X ^B ∪X ^F = ｛x ₁ ,.
x _n } and a set of variables satisfying X ^B ∩X ^F = 0. Also,

(Equation 1) Is a fully specified logical function. Set X ^B and X ^F variables are referred to as bound set and Freeset. Further, g is referred to as an image of decomposition and h is referred to as a partial function of decomposition. Simple decomposition refers to decomposition in which the output of the partial function h is 1 bit. Decomposition without overlapping variables is defined as X ^B ＸX ^F =
Decomposition that is 0, that is, decomposition where the bound set and freeset do not overlap.

As an example, a function f = x ₁ · x ′ shown in FIG.
Given the _{2 · x 3 + x '1} · x 2 · x 3 + x' 3 · x 4. Hereinafter, x ′ _i indicates negation of x _i , • indicates a logical product, and + indicates a logical sum. The function f is

(Equation 2) The presence of decomposition is indicated by the column bo as shown in FIG.
This can be checked by creating a decomposition table that maps the assignment of values to und sets and the assignment of values to free sets in rows. Since there are two types of column patterns in this decomposition table, the amount of information that can distinguish the two types from the bound set side, that is, only 1 bit is set free.
It can be seen that it should be sent to the side. Therefore, this function is
Can be decomposed as shown in

[0005] In general, in a function f, X ^B
The existence of a simple, non-overlapping decomposition with t as t and X ^F as a free set is a decomposition table in which the assignment of values to X ^B corresponds to columns and the assignment of values to X ^F corresponds to rows. You can find out by making It is checked how many types of column patterns exist in this decomposition table. If there are two types, there is decomposition, and if there are three or more types, there is no decomposition. If decomposition exists, the partial function h is bound se
It is a function that takes t as input and outputs the same value for assignments with the same column pattern in the decomposition table. The decomposition image g is a function that receives the outputs of the free set and the partial function h and outputs the same value as the original function f. In the following description, processing for determining whether or not decomposition exists for the given bound set and free set is described as processing A
Call.

In order to implement a simple and non-overlapping decomposition of the function f, it is necessary to find a bound set that gives the decomposition. For that, various bound sets
Must be performed repeatedly until the decomposition exists. Assuming that the number of variables of f is n, the number of combinations for selecting m (2 ≦ m ≦ n−1) variables from n variables is

(Equation 3) In the worst case, the processing A must be performed for this number of bound sets.

[0007]

The above decomposition table is 2 ⁿ
(N is the number of variables) because the table is of a size proportional to the number of variables. Therefore, for a logical function having a large number of variables, the storage amount and the processing time required for the process A are large. By using a sum-product representation or a BDD representation instead of a decomposition table, the amount of storage and processing time required for process A may be reduced depending on the properties of the function to be handled. Large storage capacity and processing time.

[0008] In addition, in the decomposition of the logical function, it is necessary to perform the processing A having a large storage amount and a large processing time on an enormous amount of bound sets as described above. Therefore, when decomposing a function, it is necessary to efficiently find a bound set that gives the decomposition.

[0009] The present invention has been made in view of the above,
The purpose is to detect the symmetry of variables in a function, enumerate bound sets that are likely to give decomposition, and decompose a logical function in an LSI design that can decompose a logical function efficiently and economically. It is to provide a method.

[0010]

In order to achieve the above object, according to the present invention, in an LSI design for reducing the number of logic gates, a simple and variable logic of a fully specified logic function of multiple inputs and one output is provided. When performing a decomposition without overlapping, a symmetric variable set is detected by detecting the symmetry of a variable. If there is a symmetric variable set having bi-symmetry, decomposition using an XOR gate is performed, and a univariate symmetric If there is a symmetric variable set having the property, decomposition using an AND gate is performed.
The gist is to check whether there is a decomposition to be und set.

According to the first aspect of the present invention, a symmetric variable set is obtained by detecting the symmetry of a variable.
If decomposition using gates is performed, and if there is univariate symmetry, decomposition using AND gates can be performed, and since only symmetric variable sets are not candidates for bound sets, a huge amount of bound set It is not necessary to perform the processing A on the candidates, and the processing time can be reduced.

[0012]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 shows an LSI according to an embodiment of the present invention.
FIG. 2 is a block diagram showing a configuration in a case where a logic function decomposition device that performs a logic function decomposition method in design is used in a logic design support system that operates on an electronic computer. In FIG. 1, other functional blocks of the logic design support system except for the logical function decomposing device of the present embodiment are collectively shown by reference numeral 10, and a function to be decomposed from the functional block is input. .

In the embodiment shown in FIG. 1, a symmetry detection unit 1, an XOR decomposition unit 2, an AND decomposition unit 3, and a SYM
It has a disassembly unit 4 and a function operation unit 5 for expressing logic function data on the main storage device 9 of the computer and operating the data. The function operation unit 5 includes a value substitution unit 6, a coincidence determination unit 7, and a decomposition determination unit 8.

The symmetry detecting section 1 checks the symmetry of a variable in a given function, and enumerates a set of symmetric variables if they exist. The XOR decomposition unit 2 checks whether or not a symmetric variable set having bi-symmetry exists.
Perform disassembly using a gate. The AND decomposition unit 3 checks whether a symmetric variable set having univariate symmetry exists, and
If there is, decomposition using an AND gate is performed. The SYM decomposition unit 4 checks whether a simple and variable-free decomposition such that a symmetric variable set is a bound set is possible, and if possible, performs the decomposition.

A function to be decomposed is input to the symmetry detection unit 1 from another functional block 10 in the logic design support system. When a symmetric variable set exists, the symmetry detecting unit 1 calculates a set of the function to be decomposed and the symmetric variable set by X
It is passed to the OR decomposition section 2, AND decomposition section 3, and SYM decomposition section 4. When the symmetric variable set does not exist, the fact that the decomposition did not exist is notified to other function blocks. The XOR decomposition section 2, the AND decomposition section 3, and the SYM decomposition section 4 pass whether or not decomposition has occurred and the decomposition result to another functional block.

Next, the procedure of the embodiment of FIG. 1 will be described with reference to the flowchart shown in FIG. First, the symmetry detecting unit 1 checks the symmetry of the variable in the given logical function, and lists a set of symmetric variables if they exist (steps S10 and S20). If there is no symmetric variable, the process ends as no decomposition is found (step S30). Next, in the XOR decomposition unit 2,
It is checked whether or not a symmetric variable set having bi-symmetry exists, and if so, decomposition using an XOR gate is performed, and the process is terminated (steps S40 and S50). If not, the AND decomposition unit 3 checks whether or not a symmetric variable set having univariate symmetry exists.
The disassembly is performed using the D gate, and the process is terminated (steps S60 and S70). If it does not exist, the SYM decomposition unit 4 checks whether decomposition using a symmetric variable set as a boundset is possible, and if possible, performs the decomposition (steps S80 and S90). If it is not possible, the process ends, assuming that there is no decomposition handled by the present invention (step S30).

Here, the symmetry of the two variables will be described. A function f (x ₁ ,..., X _n ) is said to be symmetric with respect to variables {x _i , x _j } when the function does not change even if x _i and x _j are exchanged. Similarly, x _i and x ′ _j (x ′ _j
If the function does not change even interchanged represents) the negation of x _j, the variable {x _i, x _'j} that is symmetric about. here,

F _xixj = f (x ₁ ,..., X _i−1 , 1, x _{i + 1} ,..., X _j−1 , 1, x _{j + 1} ,..., X _n ) (2) f _xix′j = f (x ₁ ,..., x _i−1 , 1, x _{i + 1} ,..., x _j−1 , 0, x _{j + 1} ,..., x _n ) (3) f _{x′ixj = f (x 1, ...,} x i-1, 0, x i + 1, ..., x j-1, 1, x j + 1, ..., x n) ... (4) f x'ix'j = f (x ₁ ,..., x _i−1 , 0, x _{i + 1} ,..., x _j−1 , 0, x _{j + 1} ,..., x _n ) (5) Function f variable {x _i, x _j} necessary and sufficient condition for is symmetric about is _f xix'j = f x'ixj. Similarly, necessary and sufficient condition for the function f is symmetrical with respect to the variable {x _i, x _'j} is a _f xixj = f x'ix'j. For example, the function f = x ₁ x ' ₂ x ₃ shown in FIG.
_{· X '4 + (x'} 1 + x 2 + x '3) · x 4 is, x ₁ =
By substituting 1, x ₂ = 1, it becomes x ₄ and x ′ ₁
Since x ₄ is obtained by substituting = 0, x ′ ₂ = 0, it is symmetric about {x ₁ , x ′ ₂ } from f _x1x2 = f _x′1x′2 = x ₄ . Further, it is symmetrical with respect to {x _1, x _3} from _{f x1x'3 = f x'1x3 = x 4} .

Next, a symmetric variable set will be described. A set of input variables and their negations ｛x ₁ , x ′ ₁ , ..., x _n ,
Consider a subset X of x ′ _n }. If the function f does not change for every substitution in the subset X, f is said to be symmetric about the subset X and the set X is called a symmetric variable set. The symmetric variable set can be calculated from the set of symmetry of the two variables. This is 2 for fully specified logic functions.
The symmetry of variables is due to equivalence. An example is shown below.

[0020]

Equation 5] {x _i, x _j} and {x _j, x _k} with respect to symmetry _{⇒ {x i, x j,} x k} symmetrical with respect _{... (6) {x i,} x 'j} and {x _j , x _k} with respect to symmetry _{⇒ {x i, x 'j} , x' k symmetrical with _{respect} ... (7) {x i} , x 'j} and {x _j, x' _k} with respect to symmetry ⇒ {x _i, x ' _J , x _k } symmetry (8) Here, the bisymmetric property of the symmetric variable set will be described. Function f, {x _i, x _j} and {x _i, x _'j} When is symmetrical about both, with respect to the variable x _i and x _j of being bi-symmetrical (multiform symmetric). For example, FIG.
The function f shown, since it is symmetric with respect to both the {x _1, x _2} and {x _1, x _'2}, a bi-symmetrical with respect to variable x ₁ and x _2. If the function f is bisymmetric with respect to a certain two variables included in the symmetric variable set, f is bisymmetric with respect to all pairs of variables included in the symmetric variable set. A set of symmetric variables having such a property has bi-symmetry.

Similarly, the univariate symmetry of a symmetric variable set will be described. The function f is given by f _x'ixj = f _xixj
Univariate symmetric (si respect variable x _i in the space x _j = 1
ngle-variable symmetric). Similarly, f
If _x'ix'j = f _xix'j, that a single variable symmetric with respect to the variable x _i in the space x _j = 0. For example, the function f shown in Figure 5, since it is _{f x'1x2 = f x1x'2 = x 4} ,
A single variable symmetric with respect to variable x ₁ in the spatial x ₂ = 1. Furthermore, since it is _{f x'2x'3 = f x2x'3 = x 4} , a single variable symmetric with respect to the variable x ₂ in the space x ₃ = 0.
For certain variables x _i and x _j included in the symmetric variable set,
If the function f is univariately symmetric with respect to the variable x _i in the space x _j = b (b is either 0 or 1), no matter how _xi and x _j are selected from the set of symmetric variables, the function f is univariate symmetric. Become. A set of symmetric variables having such properties has univariate symmetry.

Next, how the present embodiment is applied to a specific function will be described. First, consider the function f shown in FIG. Examining the symmetry of variables, f _x1x'2 = f _x'1x2 =
from _{x 3 + x '3 · x} 4, can be detected symmetric variable set that {x _1, x _{2}. f x1x2 = f x'1x'2 = x '} 3 · x 4
Thus, f is symmetric also with respect to {x ₁ , x ′ ₂ }, so this symmetric variable set has bi-symmetry. in this case,

(Equation 6) Thus, decomposition using an XOR gate can be performed.

Consider the function f shown in FIG. By examining the symmetry of the variables, a set of symmetric variables {x ₁ , x ′ ₂ , x ₃ } can be detected. Since f is not symmetric with respect to {x ₁ , x ₂ }, this set of symmetric variables does not have bi-symmetry. However, f _x1x2 = from _{f x '1x2 = x 4,} f is because it is single variable symmetric with respect to variable x ₁ in the spatial x ₂ = 1, the symmetric variable set has a single variable symmetry. In this case, f = (x ₁ · x ₂ '· x ₃ ) · x' ₄ + (x ₁ ·
x decomposition it is possible to perform using an AND gate and so _{'2 · x 3)' ·} x 4.

Consider a function f shown in FIG. When examining the symmetry of variables, it can be detected symmetric variable set that _{{x 1, x 2, x} 3}. f _x1x2 = x ₄ , f _x1x'2 = x ₃
from _{x 4, f x'1x2 = x 3} · x 4, f x'1x'2 = 0, the symmetrical variable set has no nor single variable symmetry bi symmetry. However, when processing A is performed with this symmetric variable set as a bound set, f = (x ₁ · x ₂ + x ₂ · x ₃ + x ₃ · x ₁ ) ·
degradable and it can be seen and so x _4.

Next, the operation of each part of the embodiment shown in FIG. 1 will be described in detail.

In the function operation unit 5, a value substitution unit 6 calculates a value obtained by substituting a value for a variable of the function f. The match determination unit 7 determines whether the two functions match.
The decomposition determining unit 8 determines whether or not there is a simple and variable-free decomposition of the given function and bound set, and if there is, performs the decomposition. That is, processing A
Do the equivalent of

The symmetry detector 1 receives a function f as an input, and
List all the symmetric variable sets in and output them. The symmetry detecting unit 1 checks all the symmetries of the two variables in the function f in step S101 and step S101.
Step S102 for obtaining a symmetric variable set based on the result of
Consists of

In step S101, all x _i (n
≧ i respect ≧ 2), f is {x _i, x _j}, or {x
_i , x ′ _j } is symmetrical, and if _j exists, _j is found under the condition that i> j, and this is found. In other _words, f xix'j = f _{x 'ixj} or _f xixj = f x'ix'j
Holds, and if there is a maximum j satisfying i> j, this is obtained. In this processing, the value substitution unit 6 and the coincidence determination unit 7 of the function operation unit 5 are used.

In step S102, step S101
By applying the transitive rule of Expressions (6) to (8) to the result of (1), a symmetric variable set is obtained. For example, in the above operation, ｛x ₅ ,
Assuming that the symmetry of two variables x ₃ ｝, {x ₄ , x ′ ₂ }, {x ₂ , x ₁ } can be confirmed, the set of symmetric variables is {x
₅ is x _3} and _{{x 4, x '2,} x' 1}.

The XOR decomposition unit 2 receives a set of a function f and a set of symmetric variables, and outputs the result if decomposition using an XOR gate is possible. The XOR decomposition unit 2 determines whether the symmetric variable set has bi-symmetry (step S20).
1 and step S202 of actually performing decomposition when it has bi-symmetry.

In step S201, it is determined whether the function f is _{bisymmetric with} respect to certain two variables x _i and x _j included in the symmetric variable set, that is, f _xix′j = f _x′ixj and f _xix′ixj
It is checked whether _xixj = _fx'ix'j holds. In this processing, the value substitution unit 6 and the coincidence determination unit 7 of the function operation unit 5 are used. If so, f is bisymmetric for all two variables in the symmetric variable set.

In step S202, a symmetric variable set having bi-symmetry is set as a bound set, and decomposition for realizing the partial function h by an XOR gate is performed. Pair x _i of all the variables included in the symmetrical variable set, f with respect to _{x j} xix'j = f x'ixj
And f _xixj = f _x'ix'j hold, so if a decomposition table is created, it will be as shown in FIG. That is, by assigning a value to a bound set where 1 is an even number and assigning a value to a bound set where 1 is an odd number,
The row pattern is divided into two types. Here, assuming that a pattern (function) of a column in which 1 is an even number is g ₀ and a pattern (function) of a column in which 1 is an odd number is g ₁ , the decomposition image g is h = 0 In this case, g ₀ is output, and when h = 1, g ₁ is output.

The AND decomposition unit 3 receives a function f and a set of symmetric variable sets as input, and outputs the result if decomposition using an AND gate is possible. The AND decomposition unit 3 determines whether the symmetric variable set has single-variable symmetry (Step S).
301, and step S302 of actually performing decomposition when having single-variable symmetry.

[0034] In step S301, there are two variables x _i are included in the symmetrical variable set, with respect to x _j, whether the function f is a single variable symmetric, i.e. _f x'ixj = f xixj or _{f x 'ix'j} = Check whether _fxix'j holds. In this processing, the value substitution unit 6 and the coincidence determination unit 7 of the function operation unit 5 are used. If so, f is univariate symmetric for all two variables included in the symmetric variable set.

In step S302, a symmetric variable set having univariate symmetry is set as a bound set, and the partial function h is ANDed.
Perform the decomposition realized with a gate and some NOT gates. Here, all variables x _i included in the symmetric variable set
, Consider f ^N , which negates some inputs to f so that the function f is univariately symmetric in the space x _i = 0. Hereinafter, instead of decomposing f, f ^N is decomposed. After the decomposition of f ^N , by adding a NOT gate to the negated input, f
Can be determined. For all pairs of variables x _i , x _{j in the} symmetric variable set

(Equation 7) Therefore, if a decomposition table is created, it is as shown in FIG. In other words, the column pattern is divided into two types by assigning a value to the bound set that is all 1 and other than that. Here, assuming that the pattern (function) of the column of all the parts being 1 is g ₁ and the pattern (function) of the columns of the other parts is g ₀ , the decomposition image g is h = 0
In this case, g ₀ is output, and when h = 1, g ₁ is output.

The SYM decomposition unit 4 receives a set of a function f and a set of symmetric variables as input, and outputs this if the decomposition can be performed with the symmetric variable set as a bound set. It is checked using the decomposition determination unit 8 of the function operation unit 5 whether the input symmetric variable set can be decomposed into a bound set, that is, whether the decomposition is equivalent to the processing A.

In the design of an LSI, it is important to realize a logic function to be realized with a smaller number of logic gates, and an n-variable logic function always includes two n-1 variable logic functions and one 3 Since it can be decomposed into variable logic functions, if this is repeated recursively, 2 ⁿ ( ^{n of} 2
), And almost all logic functions require such logic gates. In the present embodiment, in order to reduce the number of logic gates, an n-variable logic function is used. With k-variable logic function and nk +
A check is made to see if it can be decomposed into a one-variable logic function, and where possible, simple and non-overlapping decomposition is performed. Then, as a result of the decomposition, a logic function that required a logic gate proportional to the worst 2 ⁿ is realized by a logic gate proportional to the worst 2 ^k +2 ^{(n−k + 1)} .

Specifically, in FIG. 4, the original function f =
x ₁ · x ' ₂ · x ₃ + x' ₁ · x ₂ · x ₃ + x ' ₃ · x
₄ is a four-variable function, functions g and h after decomposition
Can be realized by two logical functions having a small number of inputs such as a three-variable function and a two-variable function, respectively. As a result, a logic gate proportional to worst 2 ⁴ = 16 can be realized by a logic gate proportional to worst 2 ³ +2 ² = 12.

In the present invention, the decomposition in which the symmetric variable set is a bound set is examined by examining the symmetry of the variable in the logical function. In the conventional technology, a huge number of bound se
We were looking at decompositions for t candidates. If it is an n-variable logic function, the candidates for the bound set are m (2 ≦ 2) from n variables.
There are only 2 ⁿ −n−2 combinations that select m ≦ n−1) variables. In the present invention, the main processing is to check the symmetry of all the two variables, and the number when two variables are selected from n variables is n (n-1) / 2. That is, the present invention requires less processing than the conventional method and can be executed at high speed.

Also, in the present invention, by checking whether or not a symmetric variable set further satisfies bi-symmetry or single-variable symmetry, it is possible to perform decomposition using an XOR gate or decomposition using an AND gate. Has been determined. As a result, the variable set given in a certain function is bound
It is not necessary to perform the process A for determining whether or not the decomposition to be set exists.

Although there may be a plurality of bound sets that provide a simple and non-overlapping decomposition of a variable in a certain function, it is desirable that the cost for implementing the partial function be small. In the present invention, since the analysis is first performed before the decomposition using the XOR gate or the AND gate, it is possible to preferentially find the decomposition having a small cost for realizing the partial function.

In the present invention, since the bound set is limited to only a group of symmetric variables, there is no completeness to always find a decomposition if it exists. The types of disassembly shapes that can be found are reduced. However, by applying the decomposition of the present invention recursively to the images of the decomposition, it may be possible to discover those decompositions that could not be found.

[0043]

As described above, according to the present invention,
Detecting the symmetry of a variable to obtain a symmetric variable set, and in the case where a symmetric variable set exists, decomposition using an XOR gate is performed if it has bi-symmetry, and if it has univariate symmetry, Since decomposition using an AND gate can be performed, and a set other than a symmetric variable set is not considered as a candidate for a bound set, it is not necessary to perform the processing A on a huge number of candidates for a bound set, and the processing time is shortened. Speed can be increased. Further, since the analysis is performed based on the decomposition using the XOR gate and the AND gate, the decomposition of the function can be realized at low cost.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration in a case where a logical function decomposing device that executes a method for decomposing a logical function in an LSI design according to an embodiment of the present invention is used in a logical design support system that operates on an electronic computer.

FIG. 2 is a flowchart showing a procedure of the embodiment shown in FIG.

FIG. 3 is an explanatory diagram showing a simple and non-overlapping decomposition of a variable.

FIG. 4 is an explanatory diagram showing an example of decomposition using an XOR gate.

FIG. 5 is an explanatory diagram showing an example of decomposition using an AND gate.

FIG. 6 is an explanatory diagram showing an example of decomposition using a symmetric variable set as a bound set.

FIG. 7 is an explanatory diagram showing decomposition using an XOR gate;

FIG. 8 is an explanatory diagram showing decomposition using an AND gate.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Symmetry detection part 2 XOR decomposition part 3 AND decomposition part 4 SYM decomposition part 5 Function operation part 6 Value substitution part 7 Match determination part 8 Decomposition determination part 9 Main storage device 10 Other functional blocks in a logic design support system 11 XOR gate 12 AND gate 13 NOT gate

Claims (1)

[Claims] In an LSI design for reducing the number of logic gates, when performing a simple and non-overlapping decomposition of a fully specified logical function of multiple inputs and one output, a symmetric variable set is detected by detecting the symmetry of the variable. When there is a symmetric variable set having bi-symmetry, decomposition is performed using an XOR gate. When a symmetric variable set having single-variable symmetry exists, decomposition is performed using an AND gate. And if neither exists, check whether there exists a decomposition with the symmetric variable set as a bound set.
Decomposition method of logic function in design.