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International Conference on Tools and Algorithms for the Construction and Analysis of Systems

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Ramsey-Based Analysis of Parity Automata

Ramsey-Based Analysis of Parity Automata

  • Oliver Friedmann18 &
  • Martin Lange19 
  • Conference paper
  • 1569 Accesses

  • 3 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7214)

Abstract

Parity automata are a generalisation of Büchi automata that have some interesting advantages over the latter, e.g. determinisability, succinctness and the ability to express certain acceptance conditions like the intersection of a Büchi and a co-Büchi condition directly as a parity condition. Decision problems like universality and inclusion for such automata are PSPACE-complete and have originally been tackled via explicit complementation only. Ramsey-based methods are a later development that avoids explicit complementation but relies on an application of Ramsey’s Theorem for its correctness. In this paper we develop new and explicit Ramsey-based algorithms for the universality and inclusion problem for nondeterministic parity automata. We compare them to Ramsey-based algorithms which are obtained from translating parity automata into Büchi automata first and then applying the known Ramsey-based analysis procedures to the resulting automata. We show that the speed-up in the asymptotic worst-case gained through the new and direct methods is exponential in the number of priorities in the parity automata. We also show that the new algorithms are much more efficient in practice.

Keywords

  • Temporal Logic
  • Regular Language
  • Inclusion Problem
  • Complementation Problem
  • Inclusion Test

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Ludwig-Maximilians-University, Munich, Germany

    Oliver Friedmann

  2. School of Electr. Eng. and Computer Science, University of Kassel, Germany

    Martin Lange

Authors
  1. Oliver Friedmann
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  2. Martin Lange
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Editor information

Editors and Affiliations

  1. University of California at Santa Cruz, 1156 High Street, 95064, Santa Cruz, CA, USA

    Cormac Flanagan

  2. Fakultät für Ingenieurwesen, Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Lotharstraße 65, 47057, Duisburg, Germany

    Barbara König

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Cite this paper

Friedmann, O., Lange, M. (2012). Ramsey-Based Analysis of Parity Automata. In: Flanagan, C., König, B. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2012. Lecture Notes in Computer Science, vol 7214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28756-5_6

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  • DOI: https://doi.org/10.1007/978-3-642-28756-5_6

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  • Print ISBN: 978-3-642-28755-8

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