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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 Well-structured transition system ： ウィキペディア英語版 Well-structured transition system In computer science, specifically in the field of formal verification, well-structured transition systems (WSTSs) are a general class of infinite state systems for which many verification problems are decidable, owing to the existence of a kind of order between the states of the system which is compatible with the transitions of the system. WSTS decidability results can be applied to Petri nets, lossy channel systems, and more. == Formal definition == Recall that a well-quasi-ordering $\backslash leq$ on a set $X$ is a quasi-ordering (i.e., a preorder or reflexive, transitive binary relation) such that any infinite sequence of elements $x\_0,\; x\_1,\; x\_2,\; \backslash ldots$, from $X$ contains an increasing pair $x\_i\; \backslash leq\; x\_j$ with . The set $X$ is said to be well-quasi-ordered, or shortly wqo. For our purposes, a ''transition system'' is a structure $\backslash mathcal\; S\; =\; \backslash langle\; S,\; \backslash rightarrow,\; \backslash cdots\; \backslash rangle$, where $S$ is any set (its elements are called ''states''), and $\backslash rightarrow\; \backslash subseteq\; S\; \backslash times\; S$ (its elements are called ''transitions''). In general a transition system may have additional structure like initial states, labels on transitions, accepting states, etc (indicated by the dots), but they do not concern us here. A well-structured transition system consists of a transition system $\backslash langle\; S,\; \backslash to,\; \backslash leq\; \backslash rangle$, such that * $\backslash leq\; \backslash subseteq\; S\; \backslash times\; S$ is a well-quasi-ordering on the set of states. * $\backslash leq$ is upward compatible with $\backslash to$: that is, for all transitions $s\_1\; \backslash to\; s\_2$ (by this we mean $(s\_1,\; s\_2)\; \backslash in\; \backslash to$) and for all $t\_1$ such that $s\_1\; \backslash leq\; t\_1$, there exists $t\_2$ such that $t\_1\; \backslash xrightarrow\; t\_2$ (that is, $t\_2$ can be reached from $t\_1$ by a sequence of zero or more transitions) and $s\_2\; \backslash leq\; t\_2$. 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「Well-structured transition system」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.