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 Fast Optimization Processing Method of Binary Logical Function

technical field

The invention relates to a fast optimization processing method of a binary logic function.

Background technique

Logic optimization is the basis of automatic design of digital circuits. The development of digital circuit computer aided design (Computer Aided Design, CAD) system has a profound impact on many fields of computer science. The need for reliability circuits is becoming more and more urgent. Internationally, the problem of logic optimization is a research hotspot in computer science and related fields. Logic optimization is the key technology of integrated circuit logic synthesis, and the problem of finding the optimal logic optimization based on a certain optimization goal has been proved to be NP-hard. At present, there are many ways to realize the optimization of logic functions, and the method of seeking approximate optimization is generally used. The key technology of integrated circuit logic optimization is: ① Make the total number of different "AND" expressions in the logic optimization results the least, that is, reduce the number of "AND" gates; ② reduce the number of variables contained in the "AND" expression The total number, even if the number of input terminals of the "AND" gate circuit is the least; ③ seek a formalized representation method for logic optimization.

Contents of the invention

The purpose of the present invention is to provide a simple and effective binary logic function fast optimization processing method.

Technical solution of the present invention is:

A binary logic function fast optimization processing method is characterized in that: comprising the following steps:

(1) Formation of the set of substantial original items: the set of essential original items is marked as E;

(1) The steps to generate the substantive source items are as follows:

Extend the original implicant to calculate the adjacent intersection set, the original implicant is marked as Q _i , and the adjacent intersection set is marked as: AIC(Q _i ); if Then Q _i is a redundant item, delete it from the conduction set; otherwise, send Q _i to the irrelevant set and E, and delete the item contained in Q _i from _CDC at the same time, the redundant item is identified as: Ri, lead The common set is identified as: C _ON , the unrelated set is identified as: C _DC ;

(2) Calculation method of AIC(Q _i ):

(b)在C_DC中与Q_i相交；(c)在C_ON中与Q_i相交但不包含Q_i;AIC(Q _i ) should satisfy three conditions at the same time: (a) and Q _i are adjacent items and

(b) intersect Q _i in C _DC ; (c) intersect Q _i but not include Q _i in C _ON ;

(3) Generation rules:

(a) If an item in C _ON is contained in the expanded set of Q _i , delete the item from C _ON ;

(b) If the conditions are met: Then Q _i is the real original item, send Q _i to E and C _DC , and delete it from C _ON at the same time;

(2) The formation of the relative substantive implicant set: the relative substantive implicant set is identified as: P ^* ;

(1) The steps of generating the relative substantial implicant are described as follows: the relative substantial implicant is identified as: P _i ^* ;

（C_ON∪C_DC#P_i ^*）包含的集合不多于一个则应重塑；对P_i ^*扩展进行重塑后，将之移入C_DC及P^*中，同时将之从C_ON中删除；否则，若（C_ON∪C_DC#P_i ^*）包含的集合不止一个，则选择最大的DA的集合送至C_DC及P^*中，同时将之从C_ON中删除；执行完后转至（c），直至C_ON为空；(a) Find out the set that intersects with C _DC and send it to C _ON ; (b) Reshape the set——delete redundant items from C _ON to reduce the scale of C _ON coverage; (c) If in C _ON When all the items in C _DC are not intersected with C DC or C _DC is empty, select the largest set of the smallest adjacent degree, send it to C _DC and P ^* , and delete it from C _ON at the same time, the smallest phase Neighborhood is marked as: DA; if the largest DA in C _ON is the same, select the set that intersects non-empty with other sets in C _ON , send it to C _DC and P ^* , and transfer it from C _ON Delete in; (d) For each P _i ^* in C _ON , if

(C _ON ∪C _DC #P _i ^* ) should be reshaped if it contains no more than one set; after reshaping the expansion of P _i ^* , move it into C _DC and P ^* , and remove it from C _ON delete; otherwise, if (C _ON ∪C _DC #P _i ^* ) contains more than one set, then select the largest DA set and send it to C _DC and P ^* , and delete it from C _ON at the same time; go to (c) after execution , until C _ON is empty;

(2) Generation rules:

For a set in C _ON , if a certain subset of the set is neither covered by other C _ON nor covered by C _DC , it needs to be extended so as to reshape P ^* to cover other in C _ON gather;

(3) Non-redundant coverage optimization process

(1) Non-redundant coverage optimization processing method:

Select a minimum P ^* from E, P ^* and redundant item set, so that P ^* ∪ E is still a coverage of the function; the redundant item set is identified as: R, which is the set of Ri;

(2) Generation rules:

Divide the original implicant set Q into three mutually disjoint subsets Q={E, R, P ^* }; through the above, E, R, P ^* have been formed respectively in the described method; find the minimum column coverage , select the smallest P ^* ;

(4) Formation of optimization results:

Q=P ^* ∪E.

In the case of not calculating the function complement, the present invention solves the set of essential original items by selecting a special minimum item, solves the set of relative essential implicants by reshaping the set, and then optimizes the non-redundant coverage, and finally combines the set of essential original items with the relative The merging of substantive implicant sets is the result of logic function optimization. The method of the invention is simple and convenient, and improves the efficiency and accuracy of rapid optimization of logic functions.

The present invention will be further described below in conjunction with drawings and embodiments.

Figure 1 is a diagram of the E recognition process.

Figure 2 is a schematic diagram of the identification of P ^* .

Figure 3 is a diagram of the set reshaping process

Fig. 4 is a schematic diagram of relative substantive implicants set P ^* .

Detailed ways

A fast optimization processing method for a binary logic function, comprising the following steps:

1 The formation of the set of essential source items (identified as: E)

1.1 Essentially, the steps to generate the source item are described as follows:

则Q_i为冗余项（标识为：Ri），将之从导通集（标识为：C_ON）中删除；否则将Q_i送至无关集（标识为：C_DC）及E中，同时从C_DC中删除Q_i所蕴涵的项。The original implicant (identified as: Q _i ) is extended to calculate the adjacent intersection set (identified as: AIC(Q _i )). like

Then Q _i is a redundant item (identified as: Ri), and it is deleted from the on-set (identified as: C _ON ); otherwise, Q _i is sent to the irrelevant set (identified as: C _DC ) and E, and at the same time Delete the term implied by Q _i from C _DC .

1.2 Calculation method of AIC(Q _i ):

(2)在C_DC中与Q_i相交；(3)在C_ON中与Q_i相交但不包含Q_i。AIC(Q _i ) should satisfy three conditions at the same time: (1) It is adjacent to Q _i and

(2) Intersect Q _i in C _DC ; (3) Intersect Q _i but not include Q _i in C _ON .

1.3 Generation rules:

则Q_i为实质本源项，应将Q_i送至E及C_DC中，同时从C_ON中将之删除。(1) If an item in C _ON is contained in the expanded set of Q _i , the item should be deleted from C _ON ; (2) If the conditions are met:

Then Q _i is the substantive source item, Q _i should be sent to E and C _DC , and deleted from C _ON at the same time.

2 Formation of the set of relative substantive implicants (identified as: P ^* )

2.1 The steps of generating relative substantial implicants (identified as: P _i ^* ) are described as follows:

（C_ON∪C_DC#P_i ^*）包含的集合不多于一个则应重塑。对P_i ^*扩展进行重塑后，将之移入C_DC及P^*中，同时将之从C_ON中删除；否则，若

（C_ON∪C_DC#P_i ^*）包含的集合不止一个，则选择最大的DA的集合送至C_DC及P^*中，同时将之从C_ON中删除。执行完后转至（3），直至C_ON为空。(1) Find out the set that intersects with C _DC and send it to C _ON ; (2) Reshape the set——delete redundant items from C _ON to reduce the scale of C _ON coverage; (3) If in C _ON When all the items in C _DC do not intersect with C DC or C _DC is empty, select the largest set of the smallest adjacent degree (marked as: DA), send it to C _DC and P ^* , and transfer it from C _ON Delete in C _ON ; if the largest DA in C ON is the same, you should choose the set that intersects with other sets in C _ON that is non-empty, send it to C _DC and P ^* , and delete it from C _ON at the same time. (4) For each P _i ^* in C _ON , if

(C _ON ∪C _DC #P _i ^* ) shall be reshaped if it contains no more than one collection. After reshaping the expansion of P _i ^* , move it into C _DC and P ^* , and delete it from C _ON ; otherwise, if

(C _ON ∪C _DC #P _i ^* ) contains more than one set, then select the largest DA set and send it to C _DC and P ^* , and delete it from C _ON at the same time. Go to (3) after execution until C _ON is empty.

2.2 Generation rules:

For a set in C _ON , if a certain subset of the set is neither covered by other C _ON nor covered by C _DC , it needs to be extended so as to reshape P ^* to cover other in C _ON gather.

3 No-redundancy coverage optimization process

3.1 Non-redundant coverage optimization processing method:

Select a minimum P ^* from E, P ^* and redundant item set (identified as: R, which is the set of Ri), so that P ^* ∪E is still a coverage of the function.

3.2 Generation rules:

Divide the original implicant set Q into three disjoint subsets Q={E, R, P ^* }. E, R, and P ^* have been formed, respectively, by the methods described above. To find the minimum column coverage, choose the smallest P ^* .

4 Formation of optimization results:

Q=P ^* ∪E.

Example analysis:

Example 1: Let C _ON = {0000, 0001, 1200, 1211, 1121}, C _DC = {0102}, find E.

Analysis: (1) When Q ₁ ={0000}:

∵ {0000} is expanded to {0202}

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

∴ Delete {0001} in the conduction set C _ON

∵AIC={1200, 1121, 0102}

∴

∴ $\left\{0202\right\}\⋐\mathrm{E.},$ DM={0001}

即无关集中含有Q₁所包含的项{0102}∵

That is, the irrelevant set contains the item {0102} contained in Q ₁

∴ Delete {0102} from irrelevant set (ie C _DC #{0102})

(2) When Q ₂ ={1200}:

∵ {1200} is expanded to {2200}

And ∵AIC={1121, 0202}

∴

∴ $\left\{2200\right\}\⋐\mathrm{E.},$ DM={1000}

∴ Send {2200} to E

(3) When Q ₃ ={1211}:

∵{1211} has the same form after expansion (cannot be expanded)

∴AIC={1121}

∴

∴ $\left\{1211\right\}\⋐\mathrm{E.},$ DM={1011}

∴ Send {1211} to E

(4) When Q ₄ ={1121}:

∵{1121} has the same form after expansion (cannot be expanded)

∴AIC={1211, 2200, 0202}

∴

∴ $\left\{1121\right\}\⊂⃒\mathrm{E.}$

To sum up: E={2200, 0202, 1211}

Example 2: As shown in Figure 2, find P ^* . Among them, E={0120}.

Analysis: (1) Reshape collection:

Let P ₁ ^* : {2112}

P ₁ ^* {2112} intersects C _DC

And ∵ $\left\{0111\right\}{{\&Subset;\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="140107103742.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}^{*}$ and $\left\{0111\right\}\&Subset;\left\{C_{\mathrm{ON}}{\&cup;C}_{\mathrm{DC}}\right\}$ That is, it is not covered by other sets in the conducting set or unrelated sets

∴ Expand {0111} to form {2112}

Let _P2 ^* : {1121}

_P2 ^* {1121} intersects the reshape set _P1 ^* {2112}

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

Let P ₃ ^* : {1002}

∵ P ₃ ^* {1002} intersects the reshaped set P ₂ ^* {1201}

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

Let P ₄ ^* : {1210}

∵ P ₄ ^* {1210} intersects the reshape set P ₃ ^* {1020}

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

∴ Delete _P4 ^* {1210} from the conduction set C _ON

Let P ₅ ^* : {0021}

∵P ₅ ^* {0021} is disjoint from other sets in the conducting set

∴ P ₅ ^* stays the same

(2) ∵{2112} intersects with C _DC

未被覆盖And a subset of ∵{2112}

not covered

∴ Select the largest set {2112} in the conduction set and send it to the irrelevant set C _DC and P ^* , and delete it from the conduction set C _ON

After checking, there is no set intersecting with {2112} in the conduction set C _ON

∴ From the conduction set C _ON , P ₂ ^* {1201}, P ₃ ^* {1020}, P ₅ ^* {0021} are the largest set

∵P ₃ ^* {1020}, P ₅ ^* {0021} are disjoint to the conducting set

∴ Send P ₅ ^* {0021} to C _DC and P ^* , and delete this set from C _ON

∵ For the connected set the rest of the sets are disjoint from the disjoint set

∴ Send the rest of the set to C _DC and P ^* (as shown in Figure 4)

Example 3: For a matrix that does not fully enumerate the product item set P of the MIMO logic function F, find its optimal covering set.

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 002</span>}& \mathrm{<span\; class="notranslate">\; 453</span>}\\ \mathrm{<span\; class="notranslate">\; 110</span>}& \mathrm{<span\; class="notranslate">\; 544</span>}\\ \mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 445</span>}\\ \mathrm{<span\; class="notranslate">\; 100</span>}& \mathrm{<span\; class="notranslate">\; 354</span>}\\ \mathrm{<span\; class="notranslate">\; 012</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\\ \mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 534</span>}\end{array}\right]$

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

Analysis: get original implicant M(P) and irrelevant item M(D) according to requirements, and get the product term set matrix M(G) of the extended logic function after product term expansion.

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 002</span>}& \mathrm{<span\; class="notranslate">\; 453</span>}\\ \mathrm{<span\; class="notranslate">\; 110</span>}& \mathrm{<span\; class="notranslate">\; 544</span>}\\ \mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 445</span>}\\ \mathrm{<span\; class="notranslate">\; 100</span>}& \mathrm{<span\; class="notranslate">\; 354</span>}\\ \mathrm{<span\; class="notranslate">\; 012</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\\ \mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 534</span>}\end{array}\right]$

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 002</span>}& \mathrm{<span\; class="notranslate">\; 343</span>}\\ \mathrm{<span\; class="notranslate">\; 110</span>}& \mathrm{<span\; class="notranslate">\; 433</span>}\\ \mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 334</span>}\\ \mathrm{<span\; class="notranslate">\; 100</span>}& \mathrm{<span\; class="notranslate">\; 343</span>}\\ \mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 433</span>}\end{array}\right]$

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 002</span>}& \mathrm{<span\; class="notranslate">\; 443</span>}\\ \mathrm{<span\; class="notranslate">\; 120</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\\ \mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 444</span>}\\ \mathrm{<span\; class="notranslate">\; 102</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\\ \mathrm{<span\; class="notranslate">\; 012</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\end{array}\right]$

And then according to the identification method of essential source item, redundant item and relative essential implicant item:

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 002</span>}& \mathrm{<span\; class="notranslate">\; 443</span>}\\ \mathrm{<span\; class="notranslate">\; 120</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\\ \mathrm{<span\; class="notranslate">\; 012</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\end{array}\right]$

M(G _R )=φ

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 444</span>}\\ \mathrm{<span\; class="notranslate">\; 102</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\end{array}\right]$

Then form the transfer matrix from the set of relative substantive implicants G _P

$\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

Then according to the selection of the minimum column coverage, select j=1, the first column is to select the first row of the relative relative substantive implicant set G _P , the minimum column coverage P ^* =G _P [101 444], so P ^* ∪ G _E constitutes the most Excellent coverage:

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 002</span>}& \mathrm{<span\; class="notranslate">\; 443</span>}\\ \mathrm{<span\; class="notranslate">\; 120</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\\ \mathrm{<span\; class="notranslate">\; 012</span>}& \mathrm{<span\; class="notranslate">\; 344</span>}\\ \mathrm{<span\; class="notranslate">\; 101</span>}& \mathrm{<span\; class="notranslate">\; 444</span>}\end{array}\right]$

instruction manual:

Interpretation of numbers 0-5 appearing in sets or matrices

0-input variable complement (reverse) code appears, 1-input variable source code appears, 2-input variable does not appear,

3-The product term appears in the output function, 4-The product term does not appear in the output function, 5-The product term in the output function is irrelevant.

Example: Matrix representation of logistic functions

Let F be a multi-output function, which contains n input variables and m output variables, and P is a given set of product terms. Let the vector form of p ^k ∈ P be

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cccccccc}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}& <span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}& <span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>& {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right]<span\; class="notranslate">\; ,</span>$

in $\begin{array}{cccc}{p}_1^k& p_2^k& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;& p_{\mathrm{no}}^k\end{array}$ for the input section, $\begin{array}{cccc}{p}_{\mathrm{no}+1}^k& p_{\mathrm{no}+2}^k& \&CenterDot;\&CenterDot;\&CenterDot;& p_{\mathrm{no}+m}^k\end{array}$ for the output part.

为3，否则

为4。若积项p^k为无关项，则

为5。两个部分合起来为下式：The notation of the input part, that is, 0 means the complement of the variable, 1 means the original variable, and 2 means the variable does not appear in the product term. The output part is defined as follows: if the product term p ^k does not belong to the function f _t ,

is 3, otherwise

for 4. If the product term p ^k is irrelevant, then

for 5. The two parts together form the following formula:

Example. An override for the given function is

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="140107103742.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}$

Then its matrix form is

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 121</span>}& \mathrm{<span\; class="notranslate">\; 44</span>}\\ \mathrm{<span\; class="notranslate">\; 120</span>}& \mathrm{<span\; class="notranslate">\; 43</span>}\\ \mathrm{<span\; class="notranslate">\; 110</span>}& \mathrm{<span\; class="notranslate">\; 34</span>}\\ \mathrm{<span\; class="notranslate">\; 102</span>}& \mathrm{<span\; class="notranslate">\; 34</span>}\\ \mathrm{<span\; class="notranslate">\; 021</span>}& \mathrm{<span\; class="notranslate">\; 43</span>}\\ \mathrm{<span\; class="notranslate">\; 011</span>}& \mathrm{<span\; class="notranslate">\; 44</span>}\end{array}\right]\begin{array}{c}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; .</span>$

Claims (1)

1. a binary logic function fast optimization processing method is characterized in that: comprise the following steps: (1) Formation of the set of substantial original items: the set of essential original items is marked as E; (1) The steps to generate the substantive source item are as follows: Extend the original implicant to calculate the adjacent intersection set, the original implicant is marked as Q _i , and the adjacent intersection set is marked as: AIC(Q _i ); if

Then Q _i is a redundant item, delete it from the conduction set; otherwise, send Q _i to the irrelevant set and E, and delete the item contained in Q _i from _CDC at the same time, the redundant item is identified as: Ri, lead The common set is identified as: C _ON , the unrelated set is identified as: C _DC ; (2) Calculation method of AIC(Q _i ): AIC(Q _i ) should satisfy three conditions at the same time: (a) and Q _i are adjacent items and

(b) intersect Q _i in C _DC ; (c) intersect Q _i but not include Q _i in C _ON ; (3) Generation rules: (a) If an item in C _ON is contained in the expanded set of Q _i , delete the item from C _ON ; (b) If the conditions are met:

Then Q _i is the real original item, send Q _i to E and C _DC , and delete it from C _ON at the same time; (2) The formation of the relative substantive implicant set: the relative substantive implicant set is identified as: P ^* ; (1) The steps of generating the relative substantial implicant are described as follows: the relative substantial implicant is identified as: P _i ^* ; (a) Find the set that intersects with C _DC and send it to C _ON ; (b) Reshape the set——delete redundant items from C _ON to reduce the scale of C _ON coverage; (c) If in C _ON When all the items in C _DC do not intersect with C DC or C _DC is empty, select the largest set of the smallest adjacent degree, send it to C _DC and P ^* , and delete it from C _ON at the same time, the smallest phase Neighborhood is marked as: DA; if the largest DA in C _ON is the same, select the set that intersects with other sets in C _ON that is non-empty, send it to C _DC and P ^* , and transfer it from C _ON Delete in; (d) For each P _i ^* in C _ON , if (C _ON ∪C _DC #P _i ^* ) should be reshaped if it contains no more than one set; after reshaping the expansion of P _i ^* , move it into C _DC and P ^* , and remove it from C _ON delete; otherwise, if

(C _ON ∪C _DC #P _i ^* ) contains more than one set, then select the largest DA set and send it to C _DC and P ^* , and delete it from C _ON at the same time; go to (c) after execution , until C _ON is empty; (2) Generation rules: For a set in C _ON , if a certain subset of the set is neither covered by other C _ON nor covered by C _DC , it needs to be extended so as to reshape P ^* to cover other in C _ON gather; (3) Non-redundant coverage optimization process (1) Non-redundant coverage optimization processing method: Select a minimum P ^* from E, P ^* and redundant item set, so that P ^* ∪ E is still a coverage of the function; the redundant item set is identified as: R, which is the set of Ri; (2) Generation rules: Divide the original implicant set Q into three mutually disjoint subsets Q={E, R, P ^* }; through the above, E, R, P ^* have been formed respectively in the described method; find the minimum column coverage , select the smallest P ^* ; (4) Formation of optimization results: Q=P ^* ∪E.

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