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Logical Characterizations of Bisimulations for Discrete Probabilistic Systems [chapter]

Augusto Parma, Roberto Segala
Foundations of Software Science and Computational Structures  
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

Christel Baier, Holger Hermanns, Joost-Pieter Katoen, Verena Wolf
2006 Electronical Notes in Theoretical Computer Science  
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

Vincent Danos, Josée Desharnais, François Laviolette, Prakash Panangaden
2006 Information and Computation  
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]

Adnan Aziz, Vigyan Singhal, Felice Balarin, Robert K. Brayton, Alberto L. Sangiovanni-Vincentelli
1995 Lecture Notes in Computer Science  
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

Josée Desharnais, Abbas Edalat, Prakash Panangaden
2002 Information and Computation  
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

Alessandro Abate
2013 Electronical Notes in Theoretical Computer Science  
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]

Kim Guldstrand Larsen, Radu Mardare, Prakash Panangaden
2012 Lecture Notes in Computer Science  
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

Ana Sokolova
2011 Theoretical Computer Science  
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]

Paul Wild, Lutz Schröder, Dirk Pattinson, Barbara König
2019 arXiv   pre-print
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]

Pedro D'Argenio, Pedro Sánchez Terraf, Nicolás Wolovick
2010 arXiv   pre-print
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

Valentina Castiglioni, Daniel Gebler, Simone Tini
2016 Electronic Proceedings in Theoretical Computer Science  
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  
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

Holger Hermanns, Augusto Parma, Roberto Segala, Björn Wachter, Lijun Zhang
2011 Information and Computation  
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

Luca Cardelli, Kim G. Larsen, Radu Mardare, Marc Herbstritt
2011 Annual Conference for Computer Science Logic  
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]

Marius C. Bujorianu, Manuela L. Bujorianu, Howard Barringer
2009 Lecture Notes in Computer Science  
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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