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

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STACS 2001 (STACS 2001)

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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.

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Author information

Authors and Affiliations

  1. Inst. für Informatik, Universität Stuttgart Breitwiesenstr, 20-22, D-70565, Stuttgart

    Volker Diekert & Christian Hagenah

  2. Centro de Mod. Matemático y Depto. de Ciencias de la Computación, Universidad de Chile Blanco Encalada, 2120, Santiago, Chile

    Claudio Gutiérrez

Authors
  1. Volker Diekert
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  2. Claudio Gutiérrez
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  3. Christian Hagenah
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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© 2001 Springer-Verlag Berlin Heidelberg

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Diekert, V., Gutiérrez, C., Hagenah, C. (2001). The Existential Theory of Equations with Rational Constraints in Free Groups is PSPACE—Complete. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_15

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  • DOI: https://doi.org/10.1007/3-540-44693-1_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

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