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Cancellativity in finitely presented semigroups. (English) Zbl 0682.20046
This paper considers whether or not cancellativity is decidable in finitely presented semigroups answering questions raised in a paper by R. Book [J. Symb. Comput. 3, 39-68 (1987; Zbl 0638.68091)].
Cancellativity is shown to be undecidable in semigroups presented by Thue systems even if the systems are monadic. In general, cancellativity is even undecidable in semigroups presented by Church-Rosser Thue systems, but decidable if the system is monadic. For semigroups which are presented by commutative Thue systems cancellativity is decidable; the negation is in NP if the system is canonical.
Reviewer: B.L.Madison

MSC:
20M05 Free semigroups, generators and relations, word problems
03D03 Thue and Post systems, etc.
03D40 Word problems, etc. in computability and recursion theory
20M35 Semigroups in automata theory, linguistics, etc.
68Q45 Formal languages and automata
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