翻訳と辞書 Words near each other ・ Automatic enrolment ・ Automatic equipment identification ・ Automatic exposure control ・ Automatic faucet ・ Automatic film applicator ・ Automatic fire suppression ・ Automatic firearm ・ Automatic Flowers ・ Automatic for the People ・ Automatic frequency control ・ Automatic gain control ・ Automatic gas-check ・ Automatic Generation Control ・ Automatic Generic Substitution ・ Automatic grenade launcher ・ Automatic group ・ Automatic Gun-Laying Turret ・ Automatic High ・ Automatic identification and data capture ・ Automatic Identification System ・ Automatic image annotation ・ Automatic Independent Surveillance-Privacy ・ Automatic indexing ・ Automatic Kafka ・ Automatic label placement ・ Automatic lamp changer ・ Automatic Language Translator ・ Automatic lathe ・ Automatic layout ・ Automatic link establishment Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Automatic group ： ウィキペディア英語版 Automatic group In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group, i. e. can tell if a given word representation of a group element is in a "canonical form" and can tell if two elements given in canonical words differ by a generator.〔.〕 More precisely, let ''G'' be a group and ''A'' be a finite set of generators. Then an ''automatic structure'' of ''G'' with respect to ''A'' is a set of finite-state automata:〔, Section 2.3, "Automatic Groups: Definition", pp. 45–51.〕 * the ''word-acceptor'', which accepts for every element of ''G'' at least one word in $A^\backslash ast$ representing it *''multipliers'', one for each $a\; \backslash in\; A\; \backslash cup\; \backslash$, which accept a pair (''w''1, ''w''2), for words ''w''''i'' accepted by the word-acceptor, precisely when $w\_1\; a\; =\; w\_2$ in ''G''. The property of being automatic does not depend on the set of generators.〔, Section 2.4, "Invariance under Change of Generators", pp. 52–55.〕 The concept of automatic groups generalizes naturally to automatic semigroups.〔, Section 6.1, "Semigroups and Specialized Axioms", pp. 114–116.〕 ==Properties== Automatic groups have word problem solvable in quadratic time. More strongly, a given word can actually be put into canonical form in quadratic time, based on which the word problem may be solved by testing whether the canonical forms of two words are equal.〔, Theorem 2.3.10, p. 50.〕 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「Automatic group」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.