CN103714258A - Two-valued logic function quick optimization processing method - Google Patents

Abstract

The invention discloses a two-valued logic function quick optimization processing method. The method comprises the steps of real source item set formation, relatively real implication item set formation, non-redundancy coverage optimization process and optimization result formation. According to the method, on the condition that a function complementary set is not calculated, a smallest special item is selected to solve the real source item set, a remodeling set is used for solving a real implication item set, then, non-redundancy coverage optimization is conducted, and finally the logic function optimization result is obtained after the real source item set is combined with the real implication item set. The method is simple and convenient and improves the efficiency and the accuracy of logic function quick optimization.

Description

A kind of two-valued function function rapid Optimum disposal route

Technical field

The present invention relates to a kind of two-valued function function rapid Optimum disposal route.

Background technology

Logic optimization is the basis of digital circuit Automated Design, digital circuit computer-aided design (CAD) (Computer Aided Design, CAD) development of system has far-reaching influence to the numerous areas of computer science, more and more urgent to the demand of high-speed, high integration, high complexity and high reliability circuit.In the world, the problem of logic optimization is the study hotspot of computer science and association area.Logic optimization is the comprehensive gordian technique of integrated circuit (IC) logic, asks the problem of the optimum logic optimization based on a certain optimization aim to be proved to be a NP difficult problem.There is at present several different methods can realize logical function optimization, the general method of seeking near-optimal that adopts.The gordian technique of integrated circuit (IC) logic optimization is: 1. make in logic optimization result different term “and”s (AND) expression formula sum minimum, reduce AND gate number; 2. reduce the sum of contained variable in term “and” expression formula, even if AND gate circuit input end number is minimum; 3. seek the formalization representation method of logic optimization.

Summary of the invention

The object of the present invention is to provide a kind of easy, effective two-valued function function rapid Optimum disposal route.

Technical solution of the present invention is:

A two-valued function function rapid Optimum disposal route, is characterized in that: comprise the following steps:

(1) formation of essential prime set: essential prime set identification is E;

(1) the generation step of essential prime is as follows:

Irredundant cover is expanded, calculated adjacent common factor mutually, Irredundant cover is designated Q _i, adjacent crossing set identifier is: AIC(Q _i); If q _ifor redundancy, it is concentrated and deleted from conducting; Otherwise by Q _ideliver in independent set and E, simultaneously from C _dCmiddle deletion Q _ithe item containing, redundancy is designated: Ri, conducting set identifier is: C _oN, independent set is designated: C _dC;

(2) AIC (Q _i) computing method:

AIC (Q _i) should meet 3 conditions simultaneously: (a) and Q _ieach other adjacency and

(b) at C _dCin with Q _iintersect; (c) at C _oNin with Q _iintersect but do not comprise Q _i;

(3) create-rule:

(a) if C _oNin a certain item lie in Q _iset after expansion, from C _oNin by this entry deletion;

(b) if satisfy condition: q _ifor essential prime, by Q _ideliver to E and C _dCin, simultaneously from C _oNmiddle by it deletion;

(2) formation of material implicatic item set relatively: material implicatic item set identification is relatively: P ^*;

(1) the generation step of material implicatic item is described below relatively: material implicatic item is designated relatively: P _i ^*;

(a) find out and C _dCc is delivered in crossing set _oN; (b) reinvent set---by redundancy from C _oNmiddle deletion, to reduce C _oNthe scale covering; (c) if C _oNin all items not with C _dCintersect or C _dCduring for sky, select the maximum set of minimum neighbourship degree, it is delivered to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion, minimum neighbourship degree is designated: DA; If C _oNin maximum DA identical, select and C _oNin that set of intersecting of other set non-NULL, it is delivered to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion; (d) to C _oNin each P _i ^*if,

(C _oN∪ C _dC#P _i ^*) no more than one of set comprising should reinvent; To P _i ^*after expansion is reinvented, it is moved into C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion; Otherwise, if (C _oN∪ C _dC#P _i ^*) more than one of the set that comprises, select the set of maximum DA to deliver to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion; After executing, go to (c), until C _oNfor sky;

(2) create-rule:

To C _oNin certain set, if certain subset of this set is neither by other C _oNcover, also not by C _dCcover, need to expansion, to reinvent P ^*make it to cover C _oNin other set;

(3) irredundant coverage optimization process

(1) irredundant coverage optimization disposal route:

From E, P ^*with in redundancy set, select a minimum P ^*, make P ^*∪ E is still a covering of function; Redundancy set identification is: R is the set of Ri;

(2) create-rule:

Irredundant cover set Q is divided into three mutually disjoint subset Q={E, R, P ^*; By institute above, in the method for description, form respectively and produce E, R, P ^*; Ask minimum row to cover, choose minimum P ^*;

(4) formation of optimum results:

Q=P ^*∪E。

The present invention is the in the situation that of computing function supplementary set not, by choosing special minterm, solve essential prime set, by reinventing set, solve relative material implicatic item and gather, pass through again irredundant coverage optimization, finally essential prime set is merged and is logical function optimum results with relative material implicatic item set.The inventive method is easy, has improved efficiency and the accuracy of logical function rapid Optimum.

Below in conjunction with drawings and Examples, the invention will be further described.

Fig. 1 is E identifying figure.

Fig. 2 is P ^*identification schematic diagram.

Fig. 3 is set remodeling process figure

Fig. 4 is relative material implicatic item set P ^*schematic diagram.

Embodiment

A two-valued function function rapid Optimum disposal route, comprises the following steps:

1 essential prime set (is designated: formation E)

The generation step of 1.1 essential primes is described below:

Irredundant cover (is designated: Q _i) expand, calculate adjacent common factor mutually and (be designated: AIC(Q _i)).If

q _ifor redundancy (is designated: Ri), it (is designated: C from conducting collection _oN) middle deletion; Otherwise by Q _idelivering to independent set (is designated: C _dC) and E in, simultaneously from C _dCmiddle deletion Q _ithe item containing.

1.2AIC (Q _i) computing method:

AIC (Q _i) should meet 3 conditions simultaneously: (1) and Q _ieach other adjacency and

(2) at C _dCin with Q _iintersect; (3) at C _oNin with Q _iintersect but do not comprise Q _i.

1.3 create-rules:

(1) if C _oNin a certain item lie in Q _iset after expansion, should be from C _oNin by this entry deletion; (2) if satisfy condition:

q _ifor essential prime, should be by Q _ideliver to E and C _dCin, simultaneously from C _oNmiddle by it deletion.

2 relative material implicatic item set (are designated: P ^*) formation

2.1 relative material implicatic items (are designated: P _i ^*) generation step be described below:

(1) find out and C _dCc is delivered in crossing set _oN; (2) reinvent set---by redundancy from C _oNmiddle deletion, to reduce C _oNthe scale covering; (3) if C _oNin all items not with C _dCintersect or C _dCduring for sky, select minimum neighbourship degree (be designated: maximum set DA), it is delivered to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion; If C _oNin maximum DA identical, should select and C _oNin that set of intersecting of other set non-NULL, it is delivered to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion.(4) to C _oNin each P _i ^*if,

(C _oN∪ C _dC#P _i ^*) no more than one of set comprising should reinvent.To P _i ^*after expansion is reinvented, it is moved into C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion; Otherwise, if

(C _oN∪ C _dC#P _i ^*) more than one of the set that comprises, select the set of maximum DA to deliver to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion.After executing, go to (3), until C _oNfor sky.

2.2 create-rules:

To C _oNin certain set, if certain subset of this set is neither by other C _oNcover, also not by C _dCcover, need to expansion, to reinvent P ^*make it to cover C _oNin other set.

3 irredundant coverage optimization processes

3.1 irredundant coverage optimization disposal routes:

From E, P ^*with in redundancy set (being designated: R is the set of Ri), select a minimum P ^*, make P ^*∪ E is still a covering of function.

3.2 create-rules:

Irredundant cover set Q is divided into three mutually disjoint subset Q={E, R, P ^*.By institute above, in the method for description, form respectively and produce E, R, P ^*.Ask minimum row to cover, choose minimum P ^*.

The formation of 4 optimum results:

Q=P ^*∪E。

Eample Analysis:

Example 1: establish C _oN={ 0000,0001,1200,1211,1121}, C _dC={ 0102} asks E.

Resolve: (1) works as Q ₁=during 0000}:

{ form of 0000} after expansion is { 0202} to ∵

∵ again $\left\{0001\right\}\⋐C_{\mathrm{ON}}$ And $\left\{0001\right\}\⋐\left\{0202\right\}$

∴ is by conducting collection C _oNin { 0001} deletes

∵AIC={1200，1121，0102}

∴

∴ $\left\{0202\right\}\⋐E,$ DM={0001}

∵

be in independent set, to contain Q ₁item { the 0102} comprising

∴ will { it (be C that 0102} deletes from independent set _dC#{0102})

(2) work as Q ₂=during 1200}:

{ form of 1200} after expansion is { 2200} to ∵

∵ AIC={1121 again, 0202}

∴

∴ $\left\{2200\right\}\⋐E,$ DM={1000}

∴ will { 2200} delivers in E

(3) work as Q ₃=during 1211}:

∵ { the form constant (can not be expanded) of 1211} after expansion

∴AIC={1121}

∴

∴ $\left\{1211\right\}\⋐E,$ DM={1011}

∴ will { 1211} delivers in E

(4) work as Q ₄=during 1121}:

∵ { the form constant (can not be expanded) of 1121} after expansion

∴AIC={1211，2200，0202}

∴

∴ $\left\{1121\right\}\⊂⃒E$

In sum: E={2200,0202,1211}

Example 2: as shown in Figure 2, ask P ^*.Wherein, E={0120}.

Resolve: (1) reinvents set:

If P ₁ ^*: { 2112}

P ₁ ^*{ 2112} and C _dCintersect

∵ again $\left\{0111\right\}{{\&Subset;\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="140107103742.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}^{*}$ And $\left\{0111\right\}\&Subset;\left\{C_{\mathrm{ON}}{\&cup;C}_{\mathrm{DC}}\right\}$ Not being switched on other concentrated set or independent set covers

∴ is to { 0111} expands, and forms { 2112}

If P ₂ ^*: { 1121}

P ₂ ^*1121} with reinvent set P ₁ ^*{ 2112} intersects

Make P ₂ ^*=1201}, as shown in Figure 3

If P ₃ ^*: { 1002}

∵ P ₃ ^*1002} with reinvent set P ₂ ^*{ 1201} intersects

∴ makes P ₃ ^*=1020}, as in Figure 2-4.

If P ₄ ^*: { 1210}

∵ P ₄ ^*1210} with reinvent set P ₃ ^*{ 1020} intersects

∵ again ${P_4}^{*}\left\{1210\right\}\&Subset;({{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="140107103742.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}^{*}\&cup;{P_3}^{*})$

∴ is from conducting collection C _oNmiddle deletion P ₄ ^*{ 1210}

If P ₅ ^*: { 0021}

∵ P ₅ ^*{ 0021} and conducting other set of concentrating is non-intersect

∴ P ₅ ^*remain unchanged

(2) ∵ { 2112} and C _dCintersect

∵ { the subset of 2112} again

not capped

∴ chooses the concentrated maximum set of conducting, and { 2112} delivers to independent set C _dCand P ^*in, simultaneously by it from conducting collection C _oNmiddle deletion

On inspection, conducting collection C _oNin do not exist and { the set that 2112} is crossing

∴ is from conducting collection C _oNin P ₂ ^*{ 1201}, P ₃ ^*{ 1020}, P ₅ ^*{ 0021} is maximum set

∵ P ₃ ^*{ 1020}, P ₅ ^*{ 0021} and conducting collection are non-intersect

∴ is by P ₅ ^*{ 0021} delivers to C _dCand P ^*in, and this is gathered from C _oNmiddle deletion

∵ is non-intersect for the set nothing to do with collection of conducting collection remainder

∴ delivers to C by remaining set _dCand P ^*in (as shown in Figure 4)

Example 3: for a non-matrix of enumerating the product term set P of multiple-input and multiple-output logical function F completely, ask its optimum covering to gather.

$M\left(P\right)=\left[\begin{array}{cc}002& 453\\ 110& 544\\ 101& 445\\ 100& 354\\ 012& 344\\ 101& 534\end{array}\right]$

The matrix of the product term set P of multiple-input and multiple-output logical function F

Resolve: obtain as requested Irredundant cover M (P) and outlier M (D), the product term set matrix M (G) of logical function after must expanding after product term expansion.

$M\left(P\right)=\left[\begin{array}{cc}002& 453\\ 110& 544\\ 101& 445\\ 100& 354\\ 012& 344\\ 101& 534\end{array}\right]$

$M\left(D\right)=\left[\begin{array}{cc}002& 343\\ 110& 433\\ 101& 334\\ 100& 343\\ 101& 433\end{array}\right]$

$M\left(G\right)=\left[\begin{array}{cc}002& 443\\ 120& 344\\ 101& 444\\ 102& 344\\ 012& 344\end{array}\right]$

According to the recognition methods of essential prime, redundancy, relative material implicatic item, obtain again:

$M\left(G_E\right)=\left[\begin{array}{cc}002& 443\\ 120& 344\\ 012& 344\end{array}\right]$

M(G _R)=φ

$M\left(G_P\right)=\left[\begin{array}{cc}101& 444\\ 102& 344\end{array}\right]$

Again from relative material implicatic item set G _pmiddle formation turns meaning matrix

$\stackrel{-}{B}=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$

According to minimum row, cover and select again, choose j=1, first row selects material implicatic item set G relatively _pthe minimum row of the first behavior cover P ^*=G _p[101 444], so P ^*∪ G _eform optimum covering:

$M\left(P\right)=\left[\begin{array}{cc}002& 443\\ 120& 344\\ 012& 344\\ 101& 444\end{array}\right]$

Remarks explanation:

The explanation of the digital 0-5 occurring in set or matrix

0-input variable is mended (instead) code and is occurred, the appearance of 1-input variable source code, and this input variable of 2-do not occur,

In 3-output function, product term occurs, in 4-output function, product term does not occur, in 5-output function, product term is outlier.

Example: the matrix representation of logical function

If F is a multiple output function, contain n input variable and m output variable, P is given product term set.If p ^kthe vector form of ∈ P is

$V\left(p^k\right)=\left[\begin{array}{cccccccc}{p}_1^k& p_2^k& \&CenterDot;\&CenterDot;\&CenterDot;& p_n^k& p_{n+1}^k& p_{n+2}^k& \&CenterDot;\&CenterDot;\&CenterDot;& p_{n+m}^k\end{array}\right],$

Wherein $\begin{array}{cccc}{p}_1^k& p_2^k& \&CenterDot;\&CenterDot;\&CenterDot;& p_n^k\end{array}$ For input part, $\begin{array}{cccc}{p}_{n+1}^k& p_{n+2}^k& \&CenterDot;\&CenterDot;\&CenterDot;& p_{n+m}^k\end{array}$ For output.

The representation of importation, i.e. 0 benefit that represents variable, 1 represents former variable, 2 represent that variablees do not occur in product term.Output is defined as follows: if product term p ^kdo not belong to function f _t,

be 3, otherwise

be 4.If product term p ^kfor outlier,

be 5.Two parts are following formula altogether:

Example. one of given function is covered as

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="140107103742.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=x_1{x}_3+x_1\stackrel{\&OverBar;}{x_3}+\stackrel{\&OverBar;}{x_1}{x}_3+\stackrel{\&OverBar;}{x_1}{x}_2{x}_3$

$f_2=x_1{x}_3+x_1{x}_2\stackrel{\&OverBar;}{x_3}+x_1\stackrel{\&OverBar;}{x_2}+\stackrel{\&OverBar;}{x_1}{x}_2{x}_3$

Its matrix form is

$M\left(F\right)=\left[\begin{array}{cc}121& 44\\ 120& 43\\ 110& 34\\ 102& 34\\ 021& 43\\ 011& 44\end{array}\right]\begin{array}{c}\left(1\right)\\ \left(2\right)\\ \left(3\right)\\ \left(4\right)\\ \left(5\right)\\ \left(6\right)\end{array}.$

Claims (1)

1. a two-valued function function rapid Optimum disposal route, is characterized in that: comprise the following steps:

(1) formation of essential prime set: essential prime set identification is E;

(1) the generation step of essential prime is as follows:

Irredundant cover is expanded, calculated adjacent common factor mutually, Irredundant cover is designated Q _i, adjacent crossing set identifier is: AIC(Q _i); If

q _ifor redundancy, it is concentrated and deleted from conducting; Otherwise by Q _ideliver in independent set and E, simultaneously from C _dCmiddle deletion Q _ithe item containing, redundancy is designated: Ri, conducting set identifier is: C _oN, independent set is designated: C _dC;

(2) AIC (Q _i) computing method:

AIC (Q _i) should meet 3 conditions simultaneously: (a) and Q _ieach other adjacency and

(b) at C _dCin with Q _iintersect; (c) at C _oNin with Q _iintersect but do not comprise Q _i;

(3) create-rule:

(a) if C _oNin a certain item lie in Q _iset after expansion, from C _oNin by this entry deletion;

(b) if satisfy condition:

q _ifor essential prime, by Q _ideliver to E and C _dCin, simultaneously from C _oNmiddle by it deletion;

(2) formation of material implicatic item set relatively: material implicatic item set identification is relatively: P ^*;

(1) the generation step of material implicatic item is described below relatively: material implicatic item is designated relatively: P _i ^*;

(a) find out and C _dCc is delivered in crossing set _oN; (b) reinvent set---by redundancy from C _oNmiddle deletion, to reduce C _oNthe scale covering; (c) if C _oNin all items not with C _dCintersect or C _dCduring for sky, select the maximum set of minimum neighbourship degree, it is delivered to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion, minimum neighbourship degree is designated: DA; If C _oNin maximum DA identical, select and C _oNin that set of intersecting of other set non-NULL, it is delivered to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion; (d) to C _oNin each P _i ^*if, (C _oN∪ C _dC#P _i ^*) no more than one of set comprising should reinvent; To P _i ^*after expansion is reinvented, it is moved into C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion; Otherwise, if

(C _oN∪ C _dC#P _i ^*) more than one of the set that comprises, select the set of maximum DA to deliver to C _dCand P ^*in, simultaneously by it from C _oNmiddle deletion; After executing, go to (c), until C _oNfor sky;

(2) create-rule:

To C _oNin certain set, if certain subset of this set is neither by other C _oNcover, also not by C _dCcover, need to expansion, to reinvent P ^*make it to cover C _oNin other set;

(3) irredundant coverage optimization process

(1) irredundant coverage optimization disposal route:

From E, P ^*with in redundancy set, select a minimum P ^*, make P ^*∪ E is still a covering of function; Redundancy set identification is: R is the set of Ri;

(2) create-rule:

Irredundant cover set Q is divided into three mutually disjoint subset Q={E, R, P ^*; By institute above, in the method for description, form respectively and produce E, R, P ^*; Ask minimum row to cover, choose minimum P ^*;

(4) formation of optimum results:

Q=P ^*∪E。

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