Rewriting in varieties of idempotent semigroups

Authors:
Ondřej Klíma;Miroslav Korbelář;Libor Polák
Affiliations:
Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic;Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic;Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic
Venue:
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Year:
2011

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Term rewriting and all that

Term rewriting and all that
Rewrite Systems for Varieties of Semigroups

Proceedings of the 10th International Conference on Automated Deduction

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Abstract

We consider rewriting as a tool for solving identity problems in varieties of idempotent semigroups. It is known that there exist finite canonical term rewrite systems and finite canonical word rewrite systems for only a very limited number of those varieties. We present a finite canonical conditional word rewrite system for a particular variety in which the classical approaches cannot be applied. Moreover, we obtain infinite single letter deleting rewrite systems for each join-irreducible variety.