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DOI: 10.4230/LIPIcs.FSTTCS.2012.448
URN: urn:nbn:de:0030-drops-38800
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3880/
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Forejt, Vojtech ; Jancar, Petr ; Kiefer, Stefan ; Worrell, James

Bisimilarity of Probabilistic Pushdown Automata

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Abstract

We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata (without epsilon-transitions). Our first contribution is a general construction that reduces checking bisimilarity of probabilistic transition systems to checking bisimilarity of non-deterministic transition systems. This construction directly yields decidability of bisimilarity for pPDA, as well as an elementary upper bound for the bisimilarity problem on the subclass of probabilistic basic process algebras, i.e., single-state pPDA. We further show that, with careful analysis, the general reduction can be used to prove an EXPTIME upper bound for bisimilarity of probabilistic visibly pushdown automata. Here we also provide a matching lower bound, establishing EXPTIME-completeness. Finally we prove that deciding bisimilarity of probabilistic one-counter automata, another subclass of pPDA, is PSPACE-complete. Here we use a more specialised argument to obtain optimal complexity bounds.

BibTeX - Entry

@InProceedings{forejt_et_al:LIPIcs:2012:3880,
  author =	{Vojtech Forejt and Petr Jancar and Stefan Kiefer and James Worrell},
  title =	{{Bisimilarity of Probabilistic Pushdown Automata}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) },
  pages =	{448--460},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3880},
  URN =		{urn:nbn:de:0030-drops-38800},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.448},
  annote =	{Keywords: bisimilarity, probabilistic systems, pushdown automata}
}

Keywords: bisimilarity, probabilistic systems, pushdown automata
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Issue Date: 2012
Date of publication: 10.12.2012


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