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Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions

Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions SILVIA CRAFA and FRANCESCO RANZATO, University of Padova Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] and Hermanns et al. [2011] define a probabilistic Hennessy-Milner logic interpreted over probability distributions, whose corresponding logical equivalence/preorder when restricted to Dirac distributions coincides with standard bisimulation/simulation between the states of a PLTS. This result is here extended by studying the full logical equivalence/preorder between (possibly non-Dirac) distributions in terms of a notion of bisimulation/simulation defined on an LTS whose states are distributions (dLTS). We show that the well-known spectrum of behavioral relations on nonprobabilistic LTSs as well as their corresponding logical characterizations in terms of Hennessy-Milner logic scales to the probabilistic setting when considering dLTSs. Categories and Subject Descriptors: F.1.2 [Computation by Abstract Devices]: Modes of Computation-- Parallelism and concurrency, probabilistic computation; F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs--Logics of programs; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic--Modal logic, temporal logic General Terms: Languages, Theory, Verification Additional Key Words and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions

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References (28)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2641566
Publisher site
See Article on Publisher Site

Abstract

Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions SILVIA CRAFA and FRANCESCO RANZATO, University of Padova Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] and Hermanns et al. [2011] define a probabilistic Hennessy-Milner logic interpreted over probability distributions, whose corresponding logical equivalence/preorder when restricted to Dirac distributions coincides with standard bisimulation/simulation between the states of a PLTS. This result is here extended by studying the full logical equivalence/preorder between (possibly non-Dirac) distributions in terms of a notion of bisimulation/simulation defined on an LTS whose states are distributions (dLTS). We show that the well-known spectrum of behavioral relations on nonprobabilistic LTSs as well as their corresponding logical characterizations in terms of Hennessy-Milner logic scales to the probabilistic setting when considering dLTSs. Categories and Subject Descriptors: F.1.2 [Computation by Abstract Devices]: Modes of Computation-- Parallelism and concurrency, probabilistic computation; F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs--Logics of programs; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic--Modal logic, temporal logic General Terms: Languages, Theory, Verification Additional Key Words and

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Sep 16, 2014

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