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The Algebraic Theory of Parikh Automata

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Algebraic Informatics (CAI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8080))

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Abstract

The Parikh automaton model equips a finite automaton with integer registers and imposes a semilinear constraint on the set of their final settings. Here the theory of typed monoids is used to characterize the language classes that arise algebraically. Complexity bounds are derived, such as containment of the unambiguous Parikh automata languages in NC1. Noting that DetAPA languages are positive supports of rational ℤ-series, DetAPA are further shown stronger than Parikh automata on unary langages. This suggests unary DetAPA languages as candidates for separating the two better known variants of uniform NC1.

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Author information

Authors and Affiliations

  1. DIRO at U. de Montréal and Chaire Digiteo ENS Cachan-École Polytechnique, Canada

    Michaël Cadilhac & Pierre McKenzie

  2. WSI at U. Tübingen, Germany

    Andreas Krebs

Authors
  1. Michaël Cadilhac
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  2. Andreas Krebs
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  3. Pierre McKenzie
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Editor information

Editors and Affiliations

  1. ERISCS Research Group, Parc Scientifique de, Aix-Marseille University, Luminy, 13288, Marseille CEDEX 9, France

    Traian Muntean

  2. Department of Mathematics, Aristotle University of Thessaloniki, University Campus, 54124, Thessaloniki, Greece

    Dimitrios Poulakis

  3. ERISCS Research Group and IML Research Laboratory, Parc Scientifique de, Aix-Marseille University, Luminy, 13288, Marseille, France

    Robert Rolland

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Cadilhac, M., Krebs, A., McKenzie, P. (2013). The Algebraic Theory of Parikh Automata. In: Muntean, T., Poulakis, D., Rolland, R. (eds) Algebraic Informatics. CAI 2013. Lecture Notes in Computer Science, vol 8080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40663-8_7

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  • DOI: https://doi.org/10.1007/978-3-642-40663-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40662-1

  • Online ISBN: 978-3-642-40663-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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