Decidable Approximations of Term Rewriting Systems
Decidable Approximations of Term Rewriting Systems
复制标题
术语重写系统的可判定近似
DOI：
10.1007/3-540-61464-8_65
复制
发表时间：
1996
期刊：
影响因子：
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通讯作者：
Florent Jacquemard
中科院分区：
文献类型：
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作者：
Florent Jacquemard
线性项重写系统\（\ Mathcal {r} \）正在增长，对于每个规则l→r∈\（\ Mathcal {r} \），每个由l和r共享的变量都在l中共享的每个变量。我们表明，具有正常形式的地面术语。方程理论。
A linear term rewriting system \(\mathcal{R}\)is growing when, for every rule l→r ∈ \(\mathcal{R}\), each variable which is shared by l and r occurs at depth one in l. We show that the set of ground terms having a normal form w.r.t. a growing rewrite system is recognized by a finite tree automaton. This implies in particular that reachability and sequentiality of growing rewrite systems are decidable. Moreover, the word problem is decidable for related equational theories. We prove that our conditions are actually necessary: relaxing them yields undecidability of reachability.