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Tractable Probabilistic μ-Calculus that Expresses Probabilistic Temporal Logics

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conference contribution
posted on 24.04.2015, 16:40 by P. Castro, C. Kilmurray, Nir Piterman
We revisit a recently introduced probabilistic μ-calculus and study an expressive fragment of it. By using the probabilistic quantification as an atomic operation of the calculus we establish a connection between the calculus and obligation games. The calculus we consider is strong enough to encode well-known logics such as pCTL and pCTL*. Its game semantics is very similar to the game semantics of the classical μ-calculus (using parity obligation games instead of parity games). This leads to an optimal complexity of NP intersection co-NP for its finite model checking procedure. Furthermore, we investigate a (relatively) well-behaved fragment of this calculus: an extension of pCTL with fixed points. An important feature of this extended version of pCTL is that its model checking is only exponential w.r.t. the alternation depth of fixed points, one of the main characteristics of Kozen's μ-calculus.

History

Citation

Leibniz International Proceedings in Informatics (2015) Volume 30 pp. 211-223

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Science

Source

32nd Symposium on Theoretical Aspects of Computer Science, Munich, Germany

Version

VoR (Version of Record)

Published in

Leibniz International Proceedings in Informatics (2015) Volume 30 pp. 211-223

Publisher

Leibniz Center for Informatics

issn

1868-8969

isbn

978-3-939897-78-1

Available date

24/04/2015

Publisher version

http://drops.dagstuhl.de/opus/volltexte/2015/4915/

Notes

1998 ACM Subject Classification F.4.1 Mathematical Logic

Temporal coverage: start date

04/03/2015

Temporal coverage: end date

07/03/2015

Language

en

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