Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F18%3A10241459" target="_blank" >RIV/61989100:27240/18:10241459 - isvavai.cz</a>

Alternative codes found

RIV/61989592:15310/18:73590198

Result on the web

<a href="https://lmcs.episciences.org/4972/pdf" target="_blank" >https://lmcs.episciences.org/4972/pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.23638/LMCS-14(4:13)2018" target="_blank" >10.23638/LMCS-14(4:13)2018</a>

Result language

angličtina

Original language name

Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata

Original language 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). 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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA15-13784S" target="_blank" >GA15-13784S: Computational complexity of selected verification problems</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

—

Volume of the periodical

14

Issue of the periodical within the volume

4:13

Country of publishing house

DE - GERMANY

Number of pages

25

Pages from-to

1-25

UT code for WoS article

000452745300017

EID of the result in the Scopus database

2-s2.0-85060234395