Vojtěch Forejt ; Petr Jančar ; Stefan Kiefer ; James Worrell - Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata

lmcs:4077 - Logical Methods in Computer Science, November 15, 2018, Volume 14, Issue 4 - https://doi.org/10.23638/LMCS-14(4:13)2018
Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown AutomataArticle

Authors: Vojtěch Forejt ; Petr Jančar ; Stefan Kiefer ; James Worrell

    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). We first show a general characterization of probabilistic bisimilarity in terms of two-player games, which naturally reduces checking bisimilarity of probabilistic labelled transition systems to checking bisimilarity of standard (non-deterministic) labelled transition systems. This reduction can be easily implemented in the framework of pPDA, allowing to use known results for standard (non-probabilistic) PDA and their subclasses. A direct use of the reduction incurs an exponential increase of complexity, which does not matter in deriving decidability of bisimilarity for pPDA due to the non-elementary complexity of the problem. In the cases of probabilistic one-counter automata (pOCA), of probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic process algebras (i.e., single-state pPDA) we show that an implicit use of the reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and 2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic versions. The bisimilarity problems for OCA and vPDA are known to have matching lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively); we show that these lower bounds also hold for fully probabilistic versions that do not use non-determinism.


    Volume: Volume 14, Issue 4
    Published on: November 15, 2018
    Accepted on: October 8, 2018
    Submitted on: November 18, 2017
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory

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