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Complementation of Coalgebra Automata

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Algebra and Coalgebra in Computer Science (CALCO 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5728))

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Abstract

Coalgebra automata, introduced by the second author, generalize the well-known automata that operate on infinite words/streams, trees, graphs or transition systems. This coalgebraic perspective on automata lays foundation to a universal theory of automata operating on infinite models of computation.

In this paper we prove a complementation lemma for coalgebra automata. More specifically, we provide a construction that transforms a given coalgebra automaton with parity acceptance condition into a device of similar type, which accepts exactly those pointed coalgebras that are rejected by the original automaton. Our construction works for automata operating on coalgebras for an arbitrary standard set functor which preserves weak pullbacks and restricts to finite sets.

Our proof is coalgebraic in flavour in that we introduce and use a notion of game bisimilarity between certain kinds of parity games.

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References

  1. Baltag, A.: A logic for coalgebraic simulation. In: Reichel, H. (ed.) Coalgebraic Methods in Computer Science (CMCS 2000). Electronic Notes in Theoretical Computer Science, vol. 33, pp. 41–60 (2000)

    Google Scholar 

  2. van Benthem, J.: Extensive games as process models. Journal of Logic, Language and Information 11(3), 289–313 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kurz, A., Kupke, C., Venema, Y.: Completeness of the finitary Moss logic. In: Areces, C., Goldblatt, R. (eds.) Advances in Modal Logic, vol. 7, pp. 193–217. College Publications (2008)

    Google Scholar 

  4. Kissig, C.: Satisfiability of S2S. Master’s thesis, Institute of Logic, Language and Computation, Amsterdam (2007)

    Google Scholar 

  5. Kupke, C., Venema, Y.: Coalgebraic automata theory: basic results. Logical Methods in Computer Science 4, 1–43 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Muller, D., Schupp, P.: Alternating automata on infinite trees. Theoretical Computer Science 54, 267–276 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pauly, M.: Logic for Social Software. PhD thesis, Institute of Logic, Language and Computation, Amsterdam (2001)

    Google Scholar 

  8. Rutten, J.: Universal coalgebra: A theory of systems. Theoretical Computer Science 249, 3–80 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Venema, Y.: Automata and fixed point logics for coalgebras. Electronic Notes in Theoretical Computer Science 106, 355–375 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Venema, Y.: Automata and fixed point logic: a coalgebraic perspective. Information and Computation 204, 637–678 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Christian Kissig

  2. Institute for Logic, Language, and Computation, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, Netherlands

    Yde Venema

Authors
  1. Christian Kissig
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  2. Yde Venema
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Alexander Kurz

  2. Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze, 206, 33100, Udine, Italy

    Marina Lenisa

  3. Faculty of Mathematics, Informatics and Mechanics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Andrzej Tarlecki

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© 2009 Springer-Verlag Berlin Heidelberg

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Kissig, C., Venema, Y. (2009). Complementation of Coalgebra Automata. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds) Algebra and Coalgebra in Computer Science. CALCO 2009. Lecture Notes in Computer Science, vol 5728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03741-2_7

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  • DOI: https://doi.org/10.1007/978-3-642-03741-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03740-5

  • Online ISBN: 978-3-642-03741-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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