CN103729519A

CN103729519A - Method for selecting and processing coverage solution logic function containing items based on minterm

Info

Publication number: CN103729519A
Application number: CN201410018856.1A
Authority: CN
Inventors: 邱建林; 顾翔; 陈建平; 高凌源; 李芬; 潘阳; 陈莉; 卞彩峰; 杨娜; 陆鹏程
Original assignee: Nantong University
Current assignee: Nantong University
Priority date: 2014-01-16
Filing date: 2014-01-16
Publication date: 2014-04-16

Abstract

The invention discloses a method for selecting and processing coverage solution logic function containing items based on the minterm. The method is suitable for complete listing functions and incomplete listing functions. By searching for truth values 4 in the largest number step by step, a matrix coverage is set up so that the optimal selection algorithm can be set up, all the truth values 4 of the matrix coverage are solved in an output matrix so that the coverage of a conduction set can be found, and therefore the containing items with the coverage property are generated. The method is simple and convenient to implement, and efficiency and accuracy of logic function optimization are improved.

Description

The method of selecting and processing the implication of logic function based on minimum term covering solution

技术领域technical field

本发明涉及一种基于最小项的覆盖求解逻辑函数蕴含项的选取处理方法。The invention relates to a method for selecting and processing implication items of logical function covering and solving based on minimum items.

背景技术Background technique

逻辑优化是数字电路自动设计的基础，数字电路计算机辅助设计(Computer Aided Design，CAD)系统的发展对计算机科学的诸多领域都有深远的影响，对高速度、高集成度、高复杂度和高可靠性电路的需求越来越迫切。在国际上，逻辑优化的问题是计算机科学及相关领域的研究热点。逻辑优化是集成电路逻辑综合的关键技术，求基于某一优化目标的最优逻辑优化的问题已被证明是NP难题。目前有多种方法可以实现逻辑函数优化，一般采用寻求近似优化的方法。集成电路逻辑优化的关键技术是:①使逻辑优化结果中不同“与”项（AND）表达式总数最少，即减少“与”门个数；②减少“与”项表达式中所含变量的总数，即使“与”门电路输入端个数最少；③寻求逻辑优化的形式化表示方法。Logic optimization is the basis of automatic digital circuit design. 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 the logic function, and the method of seeking approximate optimization is generally adopted. 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 formal representation method for logic optimization.

发明内容Contents of the invention

本发明的目的在于提供一种简便、效果好的一个基于最小项的覆盖求解逻辑函数蕴含项的选取处理方法。The purpose of the present invention is to provide a simple and effective method for selecting and processing the implication items of logic function covering solution based on minimum items.

本发明的技术解决方案是：Technical solution of the present invention is:

一个基于最小项的覆盖求解逻辑函数蕴含项的选取处理方法，其特征是：包括下列步骤：A method for selecting and processing the implication of logical function based on covering and solving logic function based on minimum term is characterized in that it includes the following steps:

（一）覆盖求解。计算输出矩阵覆盖，求解以最小项形式出现的矩阵其输出覆盖矩阵（或矩阵覆盖）的蕴涵项。要求找出所有真值4的导通集覆盖的蕴涵项。(1) Overlay solution. Computes the output matrix cover, solving for the implicant of the output cover matrix (or matrix cover) of a matrix in the form of a minimum term. It is required to find the implicants covered by the conduction sets of all truth values 4.

（1）覆盖的蕴涵项选取规则(1) Selection rules for covered implicants

通过逐步搜索最多数目的真值4覆盖的最多矩阵行数为构成最优覆盖标准。The maximum number of matrix rows covered by stepwise searching for the maximum number of true values 4 constitutes the optimal coverage criterion.

（2）覆盖的蕴涵项选取方法(2) Selection method of covered implicants

第一步，选取最小项形式矩阵中包含真值4个数最多的行，将其作为产生覆盖的蕴涵项的主要部分。第二步，在此基础上选取包含真值4的个数最多其覆盖行数最多的覆盖矢量作为新选取的覆盖的蕴涵项，相同真值4的个数的不同蕴涵项需分别选取。第三步，对新选取的蕴涵项其覆盖的行进行覆盖（covered）标记，并对覆盖行中的4进行假删除标记改为3，第四步，重复第一步，直至最小项形式矩阵中不包含4为止。In the first step, select the row containing the most 4 truth values in the minimum term form matrix, and use it as the main part of the implicants to generate coverage. In the second step, on this basis, the covering vector with the largest number of truth-value 4s and the largest number of covered rows is selected as the implicants of the newly selected coverage, and different implicants with the same number of truth-value 4s need to be selected separately. The third step is to mark the covered row of the newly selected implicant, and change the 4 in the covered row to a false deletion mark to 3. The fourth step is to repeat the first step until the minimum term form matrix 4 is not included.

（二）蕴涵项求解。根据选取的蕴涵项集合，计算得出各蕴涵项所包含的最小项超集。最小项超集为蕴涵项所覆盖的行的最小项（输入变量的数据表达式）集合。（三）扩展：对各蕴涵项所包含的最小项超集进行相邻项合并，将0和1扩展成2，形成最小蕴涵项。(2) Solve the implicants. According to the selected implicant set, the minimum term superset contained in each implicant is calculated. A minterm superset is the minterm (data expression of the input variables) set of rows covered by the implicant. (3) Expansion: Merge the adjacent items of the minimum superset contained in each implicant, expand 0 and 1 into 2, and form the minimum implicant.

本发明通过逐步搜索最多数目的真值4构成矩阵覆盖以构造最佳优化选取算法，通过在输出矩阵中求解矩阵覆盖所有真值4以找出导通集的覆盖，进而产生具备覆盖性质的蕴涵项。本发明方法简便，提高了逻辑函数优化的效率和准确性。The present invention constructs the optimal optimization selection algorithm by gradually searching the most number of true value 4 to form a matrix cover, and finds the cover of the conduction set by solving the matrix cover in the output matrix to generate an implication with covering properties item. The method of the invention is simple and convenient, and improves the efficiency and accuracy of logic function optimization.

附图说明Description of drawings

下面结合附图和实施例对本发明作进一步说明。The present invention will be further described below in conjunction with drawings and embodiments.

图1是输出矩阵的覆盖示意图。Figure 1 is a schematic diagram of the coverage of the output matrix.

图2是蕴涵项输出覆盖矢量m1的最小项超集示意图。Fig. 2 is a schematic diagram of the minimum term superset of the implicant output coverage vector m1.

图3是蕴涵项输出覆盖矢量m2的最小项超集示意图。Fig. 3 is a schematic diagram of the minimum term superset of the implicant output coverage vector m2.

图4是蕴涵项输出覆盖矢量m3的最小项超集示意图。Fig. 4 is a schematic diagram of the minimum term superset of the implicant output coverage vector m3.

图5是蕴涵项输出覆盖矢量m4的最小项超集示意图。Fig. 5 is a schematic diagram of the minimum term superset of the implicant output coverage vector m4.

图6是m1的扩展示意图。Fig. 6 is an expanded schematic diagram of m1.

图7是最小蕴涵项示意图。Figure 7 is a schematic diagram of the minimum implicant.

具体实施方式Detailed ways

一个基于最小项的覆盖求解逻辑函数蕴含项的选取处理方法，包括下列步骤：A method for selecting and processing the implication of logic function based on covering and solving logic function based on minimum term includes the following steps:

（1）覆盖的蕴涵项选取规则(1) Selection rules for covered implicants

（2）覆盖的蕴涵项选取方法(2) Selection method of covered implicants

实例解析：Example analysis:

例1：给出一个多输入输出逻辑函数积项矩阵表达如下。Example 1: Given a multi-input and output logic function product term matrix is expressed as follows.

$M m ((P P)) = = [\begin{matrix} 20002000 & 3434334343 \\ 12011201 & 3344333443 \\ 02100210 & 3344333443 \\ 01000100 & 3343433434 \end{matrix}]$

根据最小项形式矩阵表达要求可转化成如下形式：According to the minimum term form matrix expression requirements can be transformed into the following form:

${M m}^{' '} ((P P)) = = [\begin{matrix} 10001000 & 3434334343 \\ 00000000 & 3434334343 \\ 10011001 & 4433444334 \\ 11011101 & 4433444334 \\ 01100110 & 3344333443 \\ 00100010 & 3344333443 \\ 01000100 & 3343433434 \end{matrix}]$

例2：给出一个多输入输出逻辑函数最小项矩阵表达如下。Example 2: Given a multi-input and output logic function, the minimum term matrix is expressed as follows.

${M m}^{' '} ((P P)) = = [\begin{matrix} 110110 & 4343343433 \\ 000000 & 4334443344 \\ 011011 & 4333343333 \\ 100100 & 3333333333 \\ 101101 & 4344443444 \\ 111111 & 3443334433 \\ 001001 & 3444434444 \end{matrix}]$

首先通过在输出矩阵中求解矩阵覆盖所有真值4以找出导通集的覆盖，进而产生具备覆盖性质的蕴涵项。输出矩阵的覆盖形式如图1所示。Firstly, the cover of the conduction set is found by solving the matrix covering all truth values 4 in the output matrix, and then the implicant with the covering property is generated. The cover form of the output matrix is shown in Fig. 1.

覆盖蕴涵项选取：Override implicant selection:

该函数相应的输出矩阵包含5个输出变量、7个相关项。在输出矩阵中，选取m1、m2、m3、m4为蕴涵项为输出覆盖矢量，m1—m4覆盖了所有输出的真值4。如m1覆盖了矢量②、⑤和⑦的第四、第五个输出变量，m2覆盖了矢量⑥和⑦的第二、第三个输出变量，m3覆盖了矢量①和⑤的第一、第三个输出变量，m4覆盖了矢量②和③的第一个输出变量。The corresponding output matrix of this function contains 5 output variables and 7 related items. In the output matrix, select m1, m2, m3, m4 as the implicants as the output covering vector, and m1-m4 cover all the truth values 4 of the output. For example, m1 covers the fourth and fifth output variables of vectors ②, ⑤ and ⑦, m2 covers the second and third output variables of vectors ⑥ and ⑦, and m3 covers the first and third of vectors ① and ⑤ output variable, m4 covers the first output variable of vectors ② and ③.

蕴涵项求解：The implicants are solved:

当覆盖蕴涵项输出覆盖矢量产生后，根据输出覆盖矢量找出相应的蕴涵项，形成最小项超集。When the covering implicant output covering vector is generated, the corresponding implicant is found out according to the output covering vector to form the minimum term superset.

m1项覆盖了矢量②、⑤、⑦(见图2)。在输入矩阵中，蕴涵项输出覆盖矢量m1的候选项必定包含最小项②、⑤、⑦的超集，则蕴涵项输出覆盖矢量的最小项超集为图2所示。The m1 term covers the vectors ②, ⑤, ⑦ (see Figure 2). In the input matrix, the candidates of the implicant output coverage vector m1 must contain the superset of the minimum items ②, ⑤, ⑦, then the minimum item superset of the implicant output coverage vector is shown in Figure 2.

蕴涵项输出覆盖矢量m2、m3、m4的最小项超集分别为如图3、图4、图5所示。The minimal item supersets of the implicant output coverage vectors m2, m3, and m4 are shown in Figure 3, Figure 4, and Figure 5, respectively.

扩展：对各蕴涵项所包含的最小项超集进行相邻项合并，并将非同构的0和1扩展成2，形成最小蕴涵项。Expansion: Merge the adjacent items of the minimum superset contained in each implicant, and expand the non-isomorphic 0 and 1 into 2 to form the minimum implicant.

输出覆盖矢量m1的最小项超集扩展结果如图6所示。The results of the min-item superset expansion of the output coverage vector m1 are shown in Fig. 6.

同理，我们可以计算出m2—m4的扩展结果。合并m1—m4的扩展结果，得出逻辑函数优化最小蕴涵项结果如图7所示。Similarly, we can calculate the extended result of m2—m4. Combining the extended results of m1-m4, the result of logic function optimization minimum implicant is obtained, as shown in Figure 7.

备注说明：instruction manual:

在集合或矩阵中出现的数字0-5的解释Interpretation of numbers 0-5 appearing in sets or matrices

0-输入变量补（反）码出现，1-输入变量源码出现，2-该输入变量不出现，0-input variable complement (reverse) code appears, 1-input variable source code appears, 2-input variable does not appear,

3-输出函数中积项不出现，4-输出函数中积项出现，5-输出函数中积项为无关项。3-The product term does not appear in the output function, 4-The product term appears in the output function, 5-The product term in the output function is an irrelevant item.

1、逻辑函数的矩阵表示法1. Matrix representation of logic functions

设F为一个多输出函数，含有n个输入变量和m个输出变量，P为给定的积项集合。设p^k∈P的矢量形式为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

$V V (({p p}^{k k})) = = [[{p p}_{11}^{k k} {p p}_{22}^{k k} \cdot \cdot \cdot \cdot \cdot \cdot {p p}_{n no}^{k k} {p p}_{n no + + 11}^{k k} {p p}_{n no + + 22}^{k k} \cdot \cdot \cdot \cdot \cdot \cdot {p p}_{n no + + m m}^{k k}]],,$

其中

为输入部，

为输出部分。in

for the input section,

for the output part.

输入部分的表示法，即0表示变量之补，1表示原变量，2表示变量不在积项中出现。输出部分定义如下：若积项p^k不属于函数f_t，

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:

Claims

1. A selection processing method based on minimum term covering and solving logic function implication, it is characterized in that: comprise the following steps:

(1) Covering solution: Calculate the output matrix cover, and solve the output cover matrix or the implicant covered by the matrix in the form of the minimum term, and it is required to find all the implicants covered by the conduction set with the truth value 4;

(1) Overriding implicant selection rules

The maximum number of matrix rows covered by stepwise searching for the maximum number of true values 4 constitutes the optimal coverage criterion;

(2) Selection method of covered implicants

The first step is to select the row containing the most number of truth value 4 in the matrix of the minimum term form, and use it as the main part of the implicant to generate coverage; the second step is to select the row with the largest number of truth value 4 on this basis. The covering vector with the largest number of covered rows is used as the newly selected covering implicant, and the different implicants with the same truth value 4 need to be selected separately; the third step is to mark the covering rows of the newly selected implicant, and Change the false deletion mark to 3 in the 4 in the covered row; the fourth step, repeat the first step until the minimum term form matrix does not contain 4;

(2) Implication term solution: According to the selected implicant set, calculate the minimum term superset contained in each implicant; the minimum term superset is the minimum term set of the rows covered by the implicant;

(3) Expansion: Merge the adjacent items of the minimum superset contained in each implicant, expand 0 and 1 into 2, and form the minimum implicant.