Bisimilarity of Probabilistic Pushdown Automata

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Authors

FOREJT Vojtěch JANČAR Petr KIEFER Stefan WORRELL James

Year of publication 2012
Type Article in Proceedings
Conference FSTTCS
MU Faculty or unit

Faculty of Informatics

Citation
Web http://drops.dagstuhl.de/opus/volltexte/2012/3880/pdf/41.pdf
Field Informatics
Keywords Bisimulation; infinite state systems; stochastic system
Description 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.
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