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Logical Characterizations of Bisimulations for Discrete Probabilistic Systems
[chapter]
Foundations of Software Science and Computational Structures
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We give logical characterizations of bisimulation relations for the probabilistic automata of Segala in terms of three Hennessy-Milner style logics. ...
The three logics characterize strong, strong probabilistic and weak probabilistic bisimulation, and differ only in the kind of diamond operator used. ...
There is already a logical characterization of bisimulation for reactive systems by Larsen and Skou [10] . ...
doi:10.1007/978-3-540-71389-0_21
dblp:conf/fossacs/ParmaS07
fatcat:lvrwkmd37jhindy5wufwthvvee
Bisimulation and Simulation Relations for Markov Chains
2006
Electronical Notes in Theoretical Computer Science
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This short paper sketches the main concepts for bisimulation and simulation relations for probabilistic systems, modelled by discrete-or continuous-time Markov chains. ...
Formal notions of bisimulation and simulation relation play a central role for any kind of process algebra. ...
They fulfill several congruence properties for composition operators of probabilistic process calculi [17, 23] , have complete axiomatizations [27] , logical characterizations by means of CTL-like branching ...
doi:10.1016/j.entcs.2005.12.078
fatcat:3b4clhw5afhz5l7ppjrmo4hibi
Bisimulation and cocongruence for probabilistic systems
2006
Information and Computation
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We prove the logical characterization theorem for event bisimulation without having to invoke any of the subtle aspects of analytic spaces that feature prominently in the corresponding proof for ordinary ...
The papers by Desharnais, Edalat, and Panangaden gave a definition of bisimulation between LMPs, and gave a logical characterization of this bisimulation. ...
Vincent Danos enjoyed the company of Elham Kashefi during the course of this research. ...
doi:10.1016/j.ic.2005.02.004
fatcat:cjyjhtbbnbbyjdkndb5d6brq7a
It usually works: The temporal logic of stochastic systems
[chapter]
1995
Lecture Notes in Computer Science
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In this paper the branching time logic pCTL* is defined. pCTL* expresses quantitative bounds on the probabilities of correct behavior; it can be interpreted over discrete Markov processes. ...
We conclude by describing practical and theoretical avenues for further work. ...
For a large class of such systems, conventional logics interpreted over finite Kripke structures are insufficient. ...
doi:10.1007/3-540-60045-0_48
fatcat:jgytbviwxrcidphjfnioy6atse
Bisimulation for Labelled Markov Processes
2002
Information and Computation
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This study revealed some unexpected results, even for discrete probabilistic systems. • Bisimulation can be characterized by a very weak modal logic. ...
The main technical contribution of the paper is a logical characterization of probabilistic bisimulation. ...
We are all grateful to the referees for their careful reading of the manuscript. Prakash Panangaden would like to thank BRICS for its hospitality during the course of this work. ...
doi:10.1006/inco.2001.2962
fatcat:mtaiefuwkvbfjasstslir72p54
Approximation Metrics Based on Probabilistic Bisimulations for General State-Space Markov Processes: A Survey
2013
Electronical Notes in Theoretical Computer Science
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The focus of this work is to discuss approximation metrics between two such processes, based on the notion of probabilistic bisimulation: in particular we investigate metrics characterized by an approximate ...
This article provides a survey of approximation metrics for stochastic processes. ...
, on the notion of bisimulation for (deterministic and) probabilistic processes. ...
doi:10.1016/j.entcs.2013.12.002
fatcat:bda7mwwxzvarti2ok7wgrrkyt4
Taking It to the Limit: Approximate Reasoning for Markov Processes
[chapter]
2012
Lecture Notes in Computer Science
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We develop a fusion of logical and metrical principles for reasoning about Markov processes. ...
A key new concept is dynamically-continuous metric bisimulation which is a property of (pseudo)metrics. ...
Mardare was also supported by Sapere Aude: DFF-Young Researchers Grant 10-085054 of the Danish Council for Independent Research. ...
doi:10.1007/978-3-642-32589-2_59
fatcat:rnvtgppffnblpitev7ym6im2oe
Probabilistic systems coalgebraically: A survey
2011
Theoretical Computer Science
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We survey the work on both discrete and continuous-space probabilistic systems as coalgebras, starting with how probabilistic systems are modeled as coalgebras and followed by a discussion of their bisimilarity ...
It is interesting to note that, for different reasons, for both discrete and continuous probabilistic systems it may be more convenient to work with behavioral equivalence than with bisimilarity. ...
Acknowledgements I am grateful to the organizers of CMCS 2010 for providing me an opportunity to give a talk and publish this work. ...
doi:10.1016/j.tcs.2011.05.008
pmid:21998490
pmcid:PMC3185909
fatcat:z4iljxlfofc5jbzyg3bwxk4g5y
A van Benthem Theorem for Quantitative Probabilistic Modal Logic
[article]
2019
arXiv
pre-print
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2018 pre-print arXiv:1810.04722v1 fatcat:ef4bes2a75g6nmmad67knw3qzi
For probabilistic systems, probabilistic modal logic thus plays an analogous role to that of Hennessy-Milner logic on classical labelled transition systems. ...
In the present paper, we provide a characterization of the expressive power of probabilistic modal logic based on this observation: We prove a probabilistic analogue of the classical van Benthem theorem ...
CONCLUSIONS We established a modal characterization result for quantitative probabilistic modal logic, which states that every formula of quantitative probabilistic first-order logic that is bisimulationinvariant ...
arXiv:1810.04722v2
fatcat:wu4kpdw4d5btzmi2hiwz72fdqu
Bisimulations for Nondeterministic Labeled Markov Processes
[article]
2010
arXiv
pre-print
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We also introduce a variation of the Hennessy-Milner logic that characterizes event bisimulation and that is sound w.r.t. the other bisimulations for arbitrary NLMP. ...
systems. ...
Acknowledgments: The logic presented here has its roots on Celayes's (2006) master thesis which has been jointly supervised by the first two coauthors of this article. ...
arXiv:1011.3362v1
fatcat:v3agfsr3srhtvopkmvscufvbmm
Logical Characterization of Bisimulation Metrics
2016
Electronic Proceedings in Theoretical Computer Science
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2016 pre-print arXiv:1610.08169v1 fatcat:u2erpkyg5vek5atp3gf7es32ue
In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic variant of the Hennessy-Milner logic. ...
Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. ...
In this paper we study logical characterizations in the field of probabilistic concurrent systems. ...
doi:10.4204/eptcs.227.4
fatcat:k4h6kolaprgg3lfx724s4gbhzm
Page 5778 of Mathematical Reviews Vol. , Issue 2000h
[page]
2000
Mathematical Reviews
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We also give a numerical characterization of bisimulation, which exhibits a remarkable resemblance to the definition of probabilistic bisimulation due to Larsen-Skou and that of strong equivalence due ...
“In recent years, the effectiveness of several approaches to dis- crete event systems has been widely recognized. Logical behavior of discrete event systems can be expressed in terms of automata [P. ...
Probabilistic Logical Characterization
2011
Information and Computation
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Our focus is on logical characterization for probabilistic automata. Parma and Segala [15] solved this characterization problem for strong (probabilistic) bisimulations. ...
Technically, they extended the Hennessy-Milner logic of Larsen and Skou [2] with distribution semantics, which then enables a sound and complete characterization of bisimulation and probabilistic bisimulation ...
Finally, we thank the anonymous referees for many constructive comments which helped improve the quality of the paper considerably. ...
doi:10.1016/j.ic.2010.11.024
fatcat:hcwfttmobbbtrks6y7zmwes6z4
Continuous Markovian Logic - From Complete Axiomatization to the Metric Space of Formulas
2011
Annual Conference for Computer Science Logic
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CML characterizes stochastic bisimulation and supports the definition of a quantified extension of satisfiability relation that measures the compatibility of a model and a property. ...
The modalities of CML approximate the rates of the exponentially distributed random variables that characterize the duration of the labeled transitions. ...
In the case of probabilistic systems, probabilistic bisimulation [17] has been introduce to relate systems with identical probabilistic behaviours and probabilistic multimodal logic (PML) [16, 17, 1 ...
doi:10.4230/lipics.csl.2011.144
dblp:conf/csl/CardelliLM11
fatcat:yi2pch3n6faptpaazb6iqjob5a
A Formal Framework for User Centric Control of Probabilistic Multi-agent Cyber-Physical Systems
[chapter]
2009
Lecture Notes in Computer Science
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A full abstraction theorem is presented, and it is proved that SafAL represents a logical characterization of bisimulation. ...
In this paper, we propose a formal framework consisting of a reference model for multi-agent cyber physical systems, and a formal logic for expressing safety properties. ...
We thank the anonymous reviewers for useful comments. ...
doi:10.1007/978-3-642-02734-5_7
fatcat:3o7daoiiu5eazkpzppd6l7ix4u
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