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Existential and Positive Theories of Equations in Graph Products

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Abstract

We prove that the existential theory of equations with normalized rational constraints in a fixed graph product of finite monoids, free monoids, and free groups is PSPACE-complete. Under certain restrictions this result also holds if the graph product is part of the input. As the second main result we prove that the positive theory of equations with recognizable constraints in graph products of finite and free groups is decidable.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Stuttgart, Breitwiesenstr. 20-22, 70565, Stuttgart, Germany

    Volker Diekert & Markus Lohrey

Authors
  1. Volker Diekert
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  2. Markus Lohrey
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

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

    Afonso Ferreira

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© 2002 Springer-VerlagBerlin Heidelberg

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Diekert, V., Lohrey, M. (2002). Existential and Positive Theories of Equations in Graph Products. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_41

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  • DOI: https://doi.org/10.1007/3-540-45841-7_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

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