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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Petrick's method ： ウィキペディア英語版 Petrick's method In Boolean algebra, Petrick's method (also known as the ''branch-and-bound'' method) is a technique for determining all minimum sum-of-products solutions from a prime implicant chart. Petrick's method is very tedious for large charts, but it is easy to implement on a computer. # Reduce the prime implicant chart by eliminating the essential prime implicant rows and the corresponding columns. # Label the rows of the reduced prime implicant chart $P\_1$, $P\_2$, $P\_3$, $P\_4$, etc. # Form a logical function $P$ which is true when all the columns are covered. ''P'' consists of a product of sums where each sum term has the form $(P\_\; +\; P\_\; +$$\backslash cdots$$+\; P\_)$, where each $P\_$ represents a row covering column $i$. # Reduce $P$ to a minimum sum of products by multiplying out and applying $X\; +\; XY\; =\; X$. # Each term in the result represents a solution, that is, a set of rows which covers all of the minterms in the table. To determine the minimum solutions, first find those terms which contain a minimum number of prime implicants. # Next, for each of the terms found in step five, count the number of literals in each prime implicant and find the total number of literals. # Choose the term or terms composed of the minimum total number of literals, and write out the corresponding sums of prime implicants. Example of Petrick's method (copied from http://www.mrc.uidaho.edu/mrc/people/jff/349/lect.10) Following is the function we want to reduce: :$f(A,B,C)\; =\backslash sum\; m(0,1,2,5,6,7)\backslash ,$ The prime implicant chart from the Quine-McCluskey algorithm is as follows: | 0 1 2 5 6 7 ---------------|------------ K (0,1) a'b' | X X L (0,2) a'c' | X X M (1,5) b'c | X X N (2,6) bc' | X X P (5,7) ac | X X Q (6,7) ab | X X Based on the X marks in the table above, build a product of sums of the rows where each row is added, and columns are multiplied together: (K+L)(K+M)(L+N)(M+P)(N+Q)(P+Q) Use the distributive law to turn that expression into a sum of products. Also use the following equivalences to simplify the final expression: X + XY = X and XX = X and X+X=X = (K+L)(K+M)(L+N)(M+P)(N+Q)(P+Q) = (K+LM)(N+LQ)(P+MQ) = (KN+KLQ+LMN+LMQ)(P+MQ) = KNP + KLPQ + LMNP + LMPQ + KMNQ + KLMQ + LMNQ + LMQ Now use again the following equivalence to further reduce the equation: X + XY = X = KNP + KLPQ + LMNP + LMQ + KMNQ Choose products with fewest terms, in our example, there are two products with three terms: KNP LMQ Choose term or terms with fewest total literals. In our example, the two products both expand to 6 literals total each: KNP expands to a'b'+ bc'+ ac LMQ expands to a'c'+ b'c + ab So either one can be used. In general, application of Petricks method is tedious for large charts, but it is easy to implement on a computer. ==External links== * () Tutorial on Quine-McCluskey and Petrick's method (pdf). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Petrick's method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.