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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 disjunctive normal form ： ウィキペディア英語版 disjunctive normal form In boolean logic, a disjunctive normal form (DNF) is a standardization (or normalization) of a logical formula which is a disjunction of conjunctive clauses; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a ''cluster concept''. As a normal form, it is useful in automated theorem proving. A logical formula is considered to be in DNF if and only if it is a disjunction of one or more conjunctions of one or more literals. A DNF formula is in full disjunctive normal form if each of its variables appears exactly once in every clause. As in conjunctive normal form (CNF), the only propositional operators in DNF are and, or, and not. The ''not'' operator can only be used as part of a literal, which means that it can only precede a propositional variable. For example, all of the following formulas are in DNF: :$(A\; \backslash and\; \backslash neg\; B\; \backslash and\; \backslash neg\; C)\; \backslash or\; (\backslash neg\; D\; \backslash and\; E\; \backslash and\; F)$ :$(A\; \backslash and\; B)\; \backslash or\; C$ but and also :$A\; \backslash and\; B$ :$A\backslash !$ However, the following formulas are NOT in DNF: :$\backslash neg(A\; \backslash or\; B)$ — NOT is the outermost operator :$A\; \backslash or\; (B\; \backslash and\; (C\; \backslash or\; D))$ — an OR is nested within an AND Converting a formula to DNF involves using logical equivalences, such as the double negative elimination, De Morgan's laws, and the distributive law. All logical formulas can be converted into disjunctive normal form. However, in some cases conversion to DNF can lead to an exponential explosion of the formula. For example, in DNF, logical formulas of the following form have 2n terms: :$(X\_1\; \backslash or\; Y\_1)\; \backslash and\; (X\_2\; \backslash or\; Y\_2)\; \backslash and\; \backslash dots\; \backslash and\; (X\_n\; \backslash or\; Y\_n)$ Any particular Boolean function can be represented by one and only one full disjunctive normal form, one of the two canonical forms. An important variation used in the study of computational complexity is ''k-DNF''. A formula is in ''k-DNF'' if it is in DNF and each clause contains at most k literals. Unlike the corresponding subclasses of conjunctive normal form for k>=3, there is no easy algorithm to convert an arbitrary instance of a formula in DNF to k-DNF. The following is a formal grammar for DNF: # ''disjunct'' → (''conjunct'' ∨ ''disjunct'') # ''disjunct'' → ''conjunct'' # ''conjunct'' → (''literal'' ∧ ''conjunct'') # ''conjunct'' → ''literal'' # ''literal'' → ¬''variable'' # ''literal'' → ''variable'' Where ''variable'' is any variable. ==See also== * Algebraic normal form * Boolean function * Boolean-valued function * Conjunctive normal form * Horn clause * Karnaugh map * Logical graph * Propositional logic * Quine–McCluskey algorithm * Truth table 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「disjunctive normal form」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.