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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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  1. Institut für Formale Methoden der Informatik, Universität Stuttgart, Universitätsstraße 38, 70569 Stuttgart, Germany

    Volker Diekert & Markus Lohrey

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  1. Volker Diekert
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  2. Markus Lohrey
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Correspondence to Volker Diekert or Markus Lohrey.

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Diekert, V., Lohrey, M. Existential and Positive Theories of Equations in Graph Products. Theory Comput Systems 37, 133–156 (2004). https://doi.org/10.1007/s00224-003-1110-x

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  • DOI: https://doi.org/10.1007/s00224-003-1110-x

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