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McCammond’s normal forms for free aperiodic semigroups revisited

Part of: Semigroups Theory of computing

Published online by Cambridge University Press:  01 January 2015

J. Almeida ,
J. C. Costa  and
M. Zeitoun
J. Almeida
Affiliation:
CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal email jalmeida@fc.up.pt
J. C. Costa
Affiliation:
CMAT, Departamento de Matemática e Aplicações, Universidade do Minho, Campus de Gualtar, 4700-320 Braga, Portugal email jcosta@math.uminho.pt
M. Zeitoun
Affiliation:
LaBRI, Université Bordeaux & CNRS UMR 5800, 351 cours de la Libération, 33405 Talence Cedex, France email mz@labri.fr

Abstract

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This paper revisits the solution of the word problem for ${\it\omega}$-terms interpreted over finite aperiodic semigroups, obtained by J. McCammond. The original proof of correctness of McCammond’s algorithm, based on normal forms for such terms, uses McCammond’s solution of the word problem for certain Burnside semigroups. In this paper, we establish a new, simpler, correctness proof of McCammond’s algorithm, based on properties of certain regular languages associated with the normal forms. This method leads to new applications.

MSC classification

Primary: 20M05: Free semigroups, generators and relations, word problems 20M07: Varieties and pseudovarieties of semigroups
Secondary: 20M35: Semigroups in automata theory, linguistics, etc. 68Q70: Algebraic theory of languages and automata
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 130 - 147
Copyright
© The Author(s) 2015 

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