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On the Complexity of Semantic Equivalences for Pushdown Automata and BPA

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Mathematical Foundations of Computer Science 2002 (MFCS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2420))

Abstract

We study the complexity of comparing pushdown automata (PDA) and context-free processes (BPA) to finite-state systems, w.r.t. strong and weak simulation preorder/equivalence and strong and weak bisimulation equivalence. We present a complete picture of the complexity of all these problems. In particular, we show that strong and weak simulation preorder (and hence simulation equivalence) is EXPTIME-complete between PDA/BPA and finite-state systems in both directions. For PDA the lower bound even holds if the finite-state system is fixed, while simulation-checking between BPA and any fixed finite-state system is already polynomial. Furthermore, we show that weak (and strong) bisimilarity between PDA and finite-state systems is PSPACE-complete, while strong (and weak) bisimilarity between two PDAs is EXPTIME-hard.

Supported by the Grant Agency of the Czech Republic, grant No. 201/00/0400.

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Author information

Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Antonín Kučera

  2. Department of Computer Science, Albert-Ludwigs-University Freiburg, Georges-Koehler-Allee 51, D-79110, Freiburg, Germany

    Richard Mayr

Authors
  1. Antonín Kučera
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  2. Richard Mayr
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Krzysztof Diks  & Wojciech Rytter  & 

  2. Department of Computer Science, Liverpool University, Peach Street, Liverpool, L69 7ZF, UK

    Wojciech Rytter

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Kučera, A., Mayr, R. (2002). On the Complexity of Semantic Equivalences for Pushdown Automata and BPA. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_36

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  • DOI: https://doi.org/10.1007/3-540-45687-2_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44040-6

  • Online ISBN: 978-3-540-45687-2

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