Reference:

Vojtěch Forejt, Petr Jančar, Stefan Kiefer, and James Worrell. Bisimilarity of probabilistic pushdown automata. In Deepak D'Souza, Telikepalli Kavitha, and Jaikumar Radhakrishnan, editors, Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), Leibniz International Proceedings in Informatics (LIPIcs), pages 448–460, Hyderabad, India, 2012.

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.

Suggested BibTeX entry:

@inproceedings{12FJKW:fsttcs,
    address = {Hyderabad, India},
    author = {Vojt\v{e}ch Forejt and Petr Jan\v{c}ar and Stefan Kiefer and James Worrell},
    booktitle = {Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)},
    editor = {Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
    pages = {448--460},
    series = {Leibniz International Proceedings in Informatics (LIPIcs)},
    title = {Bisimilarity of Probabilistic Pushdown Automata},
    year = {2012}
}