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Equations in Free Semigroups with Anti-involution and Their Relation to Equations in Free Groups

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LATIN 2000: Theoretical Informatics (LATIN 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1776))

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Abstract

The main result of the paper is the reduction of the problem of satisfiability of equations in free groups to the satisfiability of equations in free semigroups with anti-involution (SGA), by a non-deterministic polynomial time transformation.

A free SGA is essentially the set of words over a given alphabet plus an operator which reverses words. We study equations in free SGA, generalizing several results known for equations in free semigroups, among them that the exponent of periodicity of a minimal solution of an equation E in free SGA is bounded by \(2^{{\cal O}(\vert E\vert)}\).

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Author information

Authors and Affiliations

  1. Computer Science Group, Dept. of Mathematics, Wesleyan University, Switzerland

    Claudio Gutiérrez

  2. Departamento de Ingeniería Matemática, D.I.M., Universidad de Chile, Chile

    Claudio Gutiérrez

Authors
  1. Claudio Gutiérrez
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Editor information

Editors and Affiliations

  1. ETH Zurich, Institute of Computational Science, CH-8092 Zurich and, Swiss Institute of Bioinformatics, Switzerland

    Gaston H. Gonnet

  2. Pedeciba Informática, Casilla de Correo 16120, Distrito 6, Montevideo, Uruguay

    Alfredo Viola

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© 2000 Springer-Verlag Berlin Heidelberg

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Gutiérrez, C. (2000). Equations in Free Semigroups with Anti-involution and Their Relation to Equations in Free Groups. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_38

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  • DOI: https://doi.org/10.1007/10719839_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67306-4

  • Online ISBN: 978-3-540-46415-0

  • eBook Packages: Springer Book Archive

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