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Practical Applications of the Alternating Cycle Decomposition

Practical Applications of the Alternating Cycle Decomposition

  • Antonio Casares  ORCID: orcid.org/0000-0002-6539-202010,
  • Alexandre Duret-Lutz  ORCID: orcid.org/0000-0002-6623-251211,
  • Klara J. Meyer  ORCID: orcid.org/0000-0003-1334-907912,
  • Florian Renkin  ORCID: orcid.org/0000-0002-5066-172611 &
  • …
  • Salomon Sickert  ORCID: orcid.org/0000-0002-0280-898113 
  • Conference paper
  • Open Access
  • First Online: 30 March 2022
  • 2045 Accesses

  • 2 Citations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13244)

Abstract

In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties and transformations of Muller automata. We present the first practical implementation of the ACD in two different tools, Owl and Spot, and adapt it to the framework of Emerson-Lei automata, i.e., \(\omega \)-automata whose acceptance conditions are defined by Boolean formulas. The ACD provides a transformation of Emerson-Lei automata into parity automata with strong optimality guarantees: the resulting parity automaton is minimal among those automata that can be obtained by duplication of states. Our empirical results show that this transformation is usable in practice. Further, we show how the ACD can generalize many other specialized constructions such as deciding typeness of automata and degeneralization of generalized Büchi automata, providing a framework of practical algorithms for \(\omega \)-automata.

Salomon Sickert is supported in part by the Deutsche Forschungsgemeinschaft (DFG) under project number 436811179, and in part funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 787367 (PaVeS)

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Authors and Affiliations

  1. LaBRI, Université de Bordeaux, Bordeaux, France

    Antonio Casares

  2. LRDE, EPITA, Le Kremlin-Bicêtre, France

    Alexandre Duret-Lutz & Florian Renkin

  3. Independent Researcher, Berlin, Germany

    Klara J. Meyer

  4. School of Computer Science and Engineering, The Hebrew University, Jerusalem, Israel

    Salomon Sickert

Authors
  1. Antonio Casares
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  2. Alexandre Duret-Lutz
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  3. Klara J. Meyer
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  4. Florian Renkin
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  5. Salomon Sickert
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Corresponding author

Correspondence to Antonio Casares .

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Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Dr. Dana Fisman

  2. University of Illinois Urbana-Champaign, Urbana, IL, USA

    Grigore Rosu

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Casares, A., Duret-Lutz, A., Meyer, K.J., Renkin, F., Sickert, S. (2022). Practical Applications of the Alternating Cycle Decomposition. In: Fisman, D., Rosu, G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2022. Lecture Notes in Computer Science, vol 13244. Springer, Cham. https://doi.org/10.1007/978-3-030-99527-0_6

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