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Bisimulation and Logical Preservation for Continuous-Time Markov Decision Processes [chapter]

Martin R. Neuhäußer, Joost-Pieter Katoen
Lecture Notes in Computer Science  
This paper introduces strong bisimulation for continuoustime Markov decision processes (CTMDPs), a stochastic model which allows for a nondeterministic choice between exponential distributions, and shows  ...  To that end, we interpret the semantics of CSL-a stochastic variant of CTL for continuous-time Markov chains-on CTMDPs and show its measuretheoretic soundness.  ...  Acknowledgements This research has been performed as part of the QUPES project that is financed by the Netherlands Organization for Scientific Research (NWO). Daniel Klink and David N.  ... 
doi:10.1007/978-3-540-74407-8_28 fatcat:4rywozzyzjdjxhmv6unn72b3y4

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.  ...  This paper surveys the results on comparative semantics of branching-time relations for time-abstract fully probabilistic systems (discrete-time Markov chains) and continuous-time Markov chains.  ... 
doi:10.1016/j.entcs.2005.12.078 fatcat:3b4clhw5afhz5l7ppjrmo4hibi

Compositional Theories of Qualitative and Quantitative Behaviour [chapter]

Ed Brinksma
2003 Lecture Notes in Computer Science  
the theory of stochastic process algebra (SPA) and its application.  ...  Compositional, hierarchical description and analysis of functional system behaviour is the domain process algebra [24, 3, 17] .  ...  For more than a decade the author has had the privilege to discuss and work on stochastic process algebraic topics with a number of great colleagues from whom he has learned a lot.  ... 
doi:10.1007/3-540-44919-1_5 fatcat:2xcbvmkuifg33nc4jwfcx5cy4a

Probabilistic systems coalgebraically: A survey

Ana Sokolova
2011 Theoretical Computer Science  
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.  ...  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  ...  Furthermore, I would like to thank Dirk Pattinson for discussions and pointers to references, Lutz Schröder for a comment during my talk at CMCS 2010, a prompt answer to a question, and just-in-time pointers  ... 
doi:10.1016/j.tcs.2011.05.008 pmid:21998490 pmcid:PMC3185909 fatcat:z4iljxlfofc5jbzyg3bwxk4g5y

Bisimulation as a logical relation

Claudio Hermida, Uday Reddy, Edmund Robinson, Alessio Santamaria
2022 Mathematical Structures in Computer Science  
We show that this approach works for the original Park–Milner bisimulation and that it extends to weak bisimulation, and branching and semi-branching bisimulation.  ...  state spaces S and T is a bisimulation if and only if the derived algebraic structures are in the logical relation automatically generated from R.  ...  If R ⊆ S × T is a total and onto z-closed relation between continuous Markov processes F : S −→ S and G: T −→ T, then R is a logical relation of continuous Markov processes if and only if R is a strong  ... 
doi:10.1017/s0960129522000020 fatcat:nyxcnwuzp5akvagmar4ivkovwa

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 foundational study is carried out for model checking SafAL formulae against Markov models. A fundamental result states that the bisimulation preserves the probabilities of the reachable state sets.  ...  We define symmetry reduction semantics and a new concept of bisimulation for agents.  ...  We thank the anonymous reviewers for useful comments.  ... 
doi:10.1007/978-3-642-02734-5_7 fatcat:3o7daoiiu5eazkpzppd6l7ix4u

Bisimulation and cocongruence for probabilistic systems

Vincent Danos, Josée Desharnais, François Laviolette, Prakash Panangaden
2006 Information and Computation  
Of course, closely related concepts were already around: for example, Markov decision processes [20] .  ...  Introduction Markov processes with continuous-state spaces or continuous time evolution (or both) arise naturally in several fields of physics, biology, economics, and computer science.  ...  Prakash Panangaden, Josée Desharnais and Franois Laviolette have all been supported by NSERC research grants.  ... 
doi:10.1016/j.ic.2005.02.004 fatcat:cjyjhtbbnbbyjdkndb5d6brq7a

Bisimulation as a Logical Relation [article]

Claudio Hermida and Uday Reddy and Edmund Robinson and Alessio Santamaria
2022 arXiv   pre-print
We show that this approach works for the original Park-Milner bisimulation and that it extends to weak bisimulation, and branching and semi-branching bisimulation.  ...  state spaces S and T is a bisimulation if and only if the derived algebraic structures are in the logical relation automatically generated from R.  ...  Consider a continuous Markov process F : S −→ ΠS, then S × S typically carries a number of continuous Markov process structures for which both projections are homomorphisms.  ... 
arXiv:2003.13542v2 fatcat:qqk7ihaujzgibcsvy55whbihbi

Model Checking for a Class of Performance Properties of Fluid Stochastic Models [chapter]

Manuela L. Bujorianu, Marius C. Bujorianu
2006 Lecture Notes in Computer Science  
We introduce a concept of bisimulation that preserves the performance measures and a metric that characterizes the bisimulation.  ...  Recently, there is an explosive development of fluid approaches to computer and distributed systems. These approaches are inherently stochastic and generate continuous state space models.  ...  Final Remarks In this paper, we have defined a new model checking strategy and a stochastic bisimulation concept for a class of Markov processes (Borel right Markov processes) based on the notions of capacity  ... 
doi:10.1007/11777830_7 fatcat:mxgp465tzrd4fmay3iwrardlju

Probabilistic Model Checking of Labelled Markov Processes via Finite Approximate Bisimulations [chapter]

Alessandro Abate, Marta Kwiatkowska, Gethin Norman, David Parker
2014 Lecture Notes in Computer Science  
This paper concerns labelled Markov processes (LMPs), probabilistic models over uncountable state spaces originally introduced by Prakash Panangaden and colleagues.  ...  probabilistic bisimulation of a given LMP, where the resulting abstraction is characterised as a finite-state labelled Markov chain (LMC).  ...  The authors are supported in part by the ERC Advanced Grant VERIWARE, the EU FP7 project HIERATIC, the EU FP7 project MoVeS, the EU FP7 Marie Curie grant MANTRAS, the EU FP7 project AMBI, and by the NWO  ... 
doi:10.1007/978-3-319-06880-0_2 fatcat:4q4rqu3rszdi3ae7s2fk2vyua4

Symmetry reduction for stochastic hybrid systems

Manuela L. Bujorianu, Joost-Pieter Katoen
2008 2008 47th IEEE Conference on Decision and Control  
We provide a rigorous mathematical foundation for the reduction technique in the continuous case and also investigate its observability perspective.  ...  Then, we generalize the notion of symmetry reduction as recently proposed for probabilistic model checking, to continuous probabilistic systems.  ...  The most known probabilistic models are: discrete-time Markov chains (DTMC), continuous-time Markov chains (CTMC), and Markov decision processes (MDP).  ... 
doi:10.1109/cdc.2008.4739086 dblp:conf/cdc/BujorianuK08 fatcat:s23wcrpz4bbxrhwtezomncb4mm

Approximating labelled Markov processes

Josée Desharnais, Vineet Gupta, Radha Jagadeesan, Prakash Panangaden
2003 Information and Computation  
yields a logic complete for reasoning about simulation for continuous-state processes.  ...  The primary technical tools that we develop to reach these results are • A variant of a finite-model theorem for the modal logic used to characterize bisimulation, and • an isomorphism between the poset  ...  We thank Falk Bartels for pointing out an error in an earlier draft. Josée Desharnais has been supported by a grant from NSERC and by funding from MITACS during the course of this work.  ... 
doi:10.1016/s0890-5401(03)00051-8 fatcat:haprjbaejnc67bxzun5cnraery

Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking

Stefan Blom, Boudewijn R. Haverkort, Matthias Kuntz, Jaco van de Pol
2008 Electronical Notes in Theoretical Computer Science  
An important result of that research is the logic CSL (continuous stochastic logic) and its corresponding model checking algorithms.  ...  In many cases, this bisimulation allows for a substantial reduction of the state space size. But, these savings in space come at the cost of an increased time complexity.  ...  The most prominent extension is the logic CSL [3] (continuous stochastic logic).  ... 
doi:10.1016/j.entcs.2008.11.012 fatcat:mzv66nsetffo5om5lhb7ycu7du

The Ins and Outs of the Probabilistic Model Checker MRMC

Joost-Pieter Katoen, Ivan S. Zapree, Ernst Moritz Hahn, Holger Hermanns, David N. Jansen
2009 2009 Sixth International Conference on the Quantitative Evaluation of Systems  
Distinguishing features of MRMC are its support for computing time-and reward-bounded reachability probabilities, (property-driven) bisimulation minimization, and precise on-the-fly steady-state detection  ...  The Markov Reward Model Checker (MRMC) is a software tool for verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their reward extensions.  ...  We thank Maneesh Khattri (Oxford Univ.), Christina Jansen (RWTH Aachen), and Tim Kemna (Univ. Twente) for their implementation efforts.  ... 
doi:10.1109/qest.2009.11 dblp:conf/qest/KatoenZHHJ09 fatcat:c2ziyci6xjcyrlq253ltcitafi

The ins and outs of the probabilistic model checker MRMC

Joost-Pieter Katoen, Ivan S. Zapreev, Ernst Moritz Hahn, Holger Hermanns, David N. Jansen
2011 Performance evaluation (Print)  
Distinguishing features of MRMC are its support for computing time-and reward-bounded reachability probabilities, (property-driven) bisimulation minimization, and precise on-the-fly steady-state detection  ...  The Markov Reward Model Checker (MRMC) is a software tool for verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their reward extensions.  ...  We thank Maneesh Khattri (Oxford Univ.), Christina Jansen (RWTH Aachen), and Tim Kemna (Univ. Twente) for their implementation efforts.  ... 
doi:10.1016/j.peva.2010.04.001 fatcat:mxrwjxdez5c2ropa5wczhxo4oa
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