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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 Alternating finite automaton ： ウィキペディア英語版 Alternating finite automaton In automata theory, an alternating finite automaton (AFA) is a nondeterministic finite automaton whose transitions are divided into ''existential'' and ''universal'' transitions. For example, let ''A'' be an alternating automaton. * For an existential transition $(q,\; a,\; q\_1\; \backslash vee\; q\_2)$, ''A'' nondeterministically chooses to switch the state to either $q\_1$ or $q\_2$, reading ''a''. Thus, behaving like a regular nondeterministic finite automaton. * For a universal transition $(q,\; a,\; q\_1\; \backslash wedge\; q\_2)$, ''A'' moves to $q\_1$ and $q\_2$, reading ''a'', simulating the behavior of a parallel machine. Note that due to the universal quantification a run is represented by a run ''tree''. ''A'' accepts a word ''w'', if there ''exists'' a run tree on ''w'' such that ''every'' path ends in an accepting state. A basic theorem states that any AFA is equivalent to a nondeterministic finite automaton (NFA) by performing a similar kind of powerset construction as it is used for the transformation of an NFA to a deterministic finite automaton (DFA). This construction converts an AFA with ''k'' states to an NFA with up to $2^k$ states. An alternative model which is frequently used is the one where Boolean combinations are represented as ''clauses''. For instance, one could assume the combinations to be in disjunctive normal form so that $\backslash \backslash \}$ would represent $q\_1\; \backslash vee\; (q\_2\; \backslash wedge\; q\_3)$. The state tt (''true'') is represented by $\backslash$ in this case and ff (''false'') by $\backslash varnothing$. This clause representation is usually more efficient. ==Formal Definition== An alternating finite automaton (AFA) is a 6-tuple, $(S(\backslash exists),\; S(\backslash forall),\; \backslash Sigma,\; \backslash delta,\; P\_0,\; F)$, where *$S(\backslash exists)$ is a finite set of existential states. Also commonly represented as $S(\backslash vee)$. *$S(\backslash forall)$ is a finite set of universal states. Also commonly represented as $S(\backslash wedge)$. *$\backslash \; \backslash Sigma$ is a finite set of input symbols. *$\backslash \; \backslash delta$ is a set of transition functions to next state $(S(\backslash exists)\; \backslash cup\; S(\backslash forall))\; \backslash times\; (\backslash Sigma\; \backslash cup\; \backslash \; )\; \backslash to\; 2^$. *$\backslash \; P\_0$ is the initial (start) state, such that $P\_0\; \backslash in\; S(\backslash exists)\; \backslash cup\; S(\backslash forall)$. *$\backslash \; F$ is a set of accepting (final) states such that $F\; \backslash subseteq\; S(\backslash exists)\; \backslash cup\; S(\backslash forall)$. 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「Alternating finite automaton」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.