Stochastic processes as concurrent constraint programs
Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
ACM Transactions on Computational Logic (TOCL)
Testing Labelled Markov Processes
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Metrics for Labeled Markov Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Weak Bisimulation is Sound and Complete for PCTL*
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
A Logic for Probabilities in Semantics
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Approximating Labeled Markov Processes
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Approximating labelled Markov processes
Information and Computation
Domain equations for probabilistic processes
Mathematical Structures in Computer Science
Semi-pullbacks and bisimulation in categories of Markov processes
Mathematical Structures in Computer Science
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
A behavioural pseudometric for probabilistic transition systems
Theoretical Computer Science - Automata, languages and programming
Bisimulation and cocongruence for probabilistic systems
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Bisimulation relations for dynamical, control, and hybrid systems
Theoretical Computer Science
Bisimulation relations for weighted automata
Theoretical Computer Science
Probabilistic Logic over Paths
Electronic Notes in Theoretical Computer Science (ENTCS)
A Demonic Approach to Information in Probabilistic Systems
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Bisimulation and cocongruence for probabilistic systems
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Approximating labelled Markov processes again!
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Continuous time and/or continuous distributions
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
A logical duality for underspecified probabilistic systems
Information and Computation
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Testing probabilistic equivalence through reinforcement learning
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Bisimulation for general stochastic hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Trace equivalence characterization through reinforcement learning
AI'06 Proceedings of the 19th international conference on Advances in Artificial Intelligence: Canadian Society for Computational Studies of Intelligence
Bisimulation Metrics for Continuous Markov Decision Processes
SIAM Journal on Computing
Dexter kozen's influence on the theory of labelled markov processes
Logic and Program Semantics
Analysis and control of fuzzy discrete event systems using bisimulation equivalence
Theoretical Computer Science
Approximating Markov Processes by Averaging
Journal of the ACM (JACM)
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In this paper we introduce a new class of labelled transition systems; Labelled Markov Processes, and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems but the state space is a Polish space (the underlying topological space for a complete separable metric space), like the reals. Such systems are increasingly important for the study of hybrid systems. The mathematical theory of such systems is completely new from the point of view of the extant literature on probabilistic process algebra; of course it uses classical ideas from measure theory and Markov process theory. The notion of bisimulation builds on the ideas of Larsen and Skou and of Joyal, Nielsen and Winskel. The main result that we prove is that a notion of bisimulation for Markov processes on Polish spaces, which extends the Larsen-Skou definition for discrete systems, is indeed an equivalence relation. This turns out to be a rather hard mathematical result which, as far as we know, embodies a new result in pure probability theory. The mathematical ideas that we found useful are likely to be part of many future investigations of hybrid stochastic systems.