The Existential Theory of Equations with Rational Constraints in Free Groups is PSPACE—Complete

  • Volker Diekert
  • Claudio Gutiérrez
  • Christian Hagenah
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)

Abstract

This paper extends extends known results on the complexity of word equations and equations in free groups in order to include the presence of rational constraints, i.e., such that a possible solution has to respect a specification given by a rational language. Our main result states that the existential theory of equations with rational constraints in free groups is PSPACE-complete.

Keywords

Formal languages equations regular language free group 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Volker Diekert
    • 1
  • Claudio Gutiérrez
    • 2
  • Christian Hagenah
    • 1
  1. 1.Inst. für InformatikUniversität Stuttgart BreitwiesenstrStuttgart
  2. 2.Centro de Mod. Matemático y Depto. de Ciencias de la ComputaciónUniversidad de Chile Blanco EncaladaSantiagoChile

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