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Feasible Automata for Two-Variable Logic with Successor on Data Words

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Language and Automata Theory and Applications (LATA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7183))

Abstract

We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data automata. It is strictly less expressive than data automata and the expressive power is incomparable with register automata. The expressive power of weak data automata corresponds exactly to existential monadic second order logic with successor + 1 and data value equality ~, EMSO2( + 1,~). It follows from previous work, David, et. al. in 2010, that the nonemptiness problem for weak data automata can be decided in 2-NEXPTIME. Furthermore, we study weak Büchi automata on data ω-strings. They can be characterized by the extension of EMSO2( + 1,~) with existential quantifiers for infinite sets. Finally, the same complexity bound for its nonemptiness problem is established by a nondeterministic polynomial time reduction to the nonemptiness problem of weak data automata.

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Author information

Authors and Affiliations

  1. Technical University of Dortmund, Germany

    Ahmet Kara & Thomas Schwentick

  2. University of Edinburgh, UK

    Tony Tan

Authors
  1. Ahmet Kara
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  2. Thomas Schwentick
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  3. Tony Tan
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

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Kara, A., Schwentick, T., Tan, T. (2012). Feasible Automata for Two-Variable Logic with Successor on Data Words. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_30

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  • DOI: https://doi.org/10.1007/978-3-642-28332-1_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28331-4

  • Online ISBN: 978-3-642-28332-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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