Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
One-parameter semigroups of postive operators
One-parameter semigroups of postive operators
Bisimulation through probabilistic testing
Information and Computation
Bisimulation for probabilistic transition systems: a coalgebraic approach
Theoretical Computer Science
Towards Quantitative Verification of Probabilistic Transition Systems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
An Algorithm for Quantitative Verification of Probabilistic Transition Systems
CONCUR '01 Proceedings of the 12th International Conference on Concurrency Theory
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Bisimulation for Labelled Markov Processes
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A Logical Characterization of Bisimulation for Labeled Markov Processes
LICS '98 Proceedings of the 13th 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
Labelled Markov Processes: Stronger and Faster Approximations
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Approximating labelled Markov processes
Information and Computation
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 hierarchy of probabilistic system types
Theoretical Computer Science - Selected papers of CMCS'03
An approximation algorithm for labelled Markov processes: towards realistic approximation
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Stochastic Relations
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Bisimulation and cocongruence for probabilistic systems
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Labelled Markov Processes
Stochastic Coalgebraic Logic
An intrinsic characterization of approximate probabilistic bisimilarity
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Semi-pullbacks and bisimulations in categories of stochastic relations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Simulation hemi-metrics between infinite-state stochastic games
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Prevision domains and convex powercones
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Stochastic transition systems for continuous state spaces and non-determinism
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Testing semantics: connecting processes and process logics
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Continuous capacities on continuous state spaces
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Normally, one thinks of probabilistic transition systems as taking an initial probability distribution over the state space into a new probability distribution representing the system after a transition. We, however, take a dual view of Markov processes as transformers of bounded measurable functions. This is very much in the same spirit as a “predicate-transformer” view, which is dual to the state-transformer view of transition systems. We redevelop the theory of labelled Markov processes from this viewpoint; in particular, we explore approximation theory. We obtain three main results. (i) It is possible to define bisimulation on general measure spaces and show that it is an equivalence relation. The logical characterization of bisimulation can be done straightforwardly and generally. (ii) A new and flexible approach to approximation based on averaging can be given. This vastly generalizes and streamlines the idea of using conditional expectations to compute approximations. (iii) We show that there is a minimal process bisimulation-equivalent to a given process, and this minimal process is obtained as the limit of the finite approximants.