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

lmcs:4077 - Logical Methods in Computer Science, November 15, 2018, Volume 14, Issue 4
Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata

Authors: Forejt, Vojtěch and Jančar, Petr and Kiefer, Stefan and Worrell, James

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.


Source : oai:arXiv.org:1711.06120
DOI : 10.23638/LMCS-14(4:13)2018
Volume: Volume 14, Issue 4
Published on: November 15, 2018
Submitted on: November 18, 2017
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory


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