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Elements of finite order for finite monadic Church-Rosser Thue systems. (English) Zbl 0583.20054
Let T be a Thue system over S. The relation \(\leftrightarrow_ T\) is defined for \(u,v\in S^*\) by \(u\leftrightarrow_ Tv\) iff \(\exists x,y\in S^*\), (\(\ell,r)\in T:\) \((u=x\ell y\) and \(v=xry)\) or \((u=xry\) and \(v=x\ell y)\). The reflexive and transitive closure of \(\leftrightarrow_ T\) is denoted by \(\leftrightarrow^*_ T\). A Thue system T over S allows nontrivial elements of finite order if there exist \(u\in S^*\) and integers \(n\geq 0\) and \(k\geq 1\) such that \(u\leftrightarrow^*_ T\ell\) and \(u^{n+k}\leftrightarrow^*_ Tu^ n\), where \(\ell\) is the empty word. The following decision problem is shown to be decidable: for a finite monadic Church-Rosser Thue system T over S, does T allow nontrivial elements of finite order?
Reviewer: J.Grzymala-Busse

MSC:
20M35 Semigroups in automata theory, linguistics, etc.
68Q45 Formal languages and automata
20M05 Free semigroups, generators and relations, word problems
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