The equational theory of regular words

Authors:
Stephen L. Bloom;Zoltán Ésik
Affiliations:
Department of Computer Science, Stevens Institute of Technology, Hoboken, NJ;Rovira i Virgili University, Tarragona, Spain and Institute for Informatics, University of Szeged, Szeged, Hungary
Venue:
Information and Computation
Year:
2005

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Abstract

Courcelle introduced the study of regular words, i.e., words isomorphic to frontiers of regular trees. Heilbrunner showed that a nonempty word is regular if it can be generated from the singletons by the operations of concatenation, omega power, omega-op power, and the infinite family of shuffle operations. We prove that the algebra of nonempty regular words on the set A, equipped with these operations, is freely generated by A in a variety which is axiomatizable by an infinite collection of some natural equations. We also show that this variety has no finite equational basis and that its equational theory is decidable in polynomial time.