The equational theory of regular words

Stephen L. Bloom, Z. Ésik

Research output: Contribution to journalArticle

25 Citations (Scopus)

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 iff 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.

Original languageEnglish
Pages (from-to)55-89
Number of pages35
JournalInformation and Computation
Volume197
Issue number1-2
DOIs
Publication statusPublished - Feb 25 2005

Fingerprint

Equational Theory
Algebra
Polynomials
Shuffle
Concatenation
Polynomial time
Isomorphic

Keywords

  • Arrangement
  • Equational theory
  • Linear order
  • Regular
  • Word

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

The equational theory of regular words. / Bloom, Stephen L.; Ésik, Z.

In: Information and Computation, Vol. 197, No. 1-2, 25.02.2005, p. 55-89.

Research output: Contribution to journalArticle

Bloom, Stephen L. ; Ésik, Z. / The equational theory of regular words. In: Information and Computation. 2005 ; Vol. 197, No. 1-2. pp. 55-89.
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