Bisimulation through probabilistic testing
Information and Computation
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ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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CONCUR '94 Proceedings of the 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
Labelled Markov Processes: Stronger and Faster Approximations
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Labelled markov processes
Domain equations for probabilistic processes
Mathematical Structures in Computer Science
Non-additive measures by interval probability functions
Information Sciences—Informatics and Computer Science: An International Journal
Fuzzy Sets and Systems
Least Upper Bounds for Probability Measures and Their Applications to Abstractions
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Approximating Markov Processes by Averaging
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
A Demonic Approach to Information in Probabilistic Systems
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Nondeterministic Labeled Markov Processes: Bisimulations and Logical Characterization
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
Bisimulation and cocongruence for probabilistic systems
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Logical characterizations of bisimulations for discrete probabilistic systems
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
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FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Don’t know in probabilistic systems
SPIN'06 Proceedings of the 13th international conference on Model Checking Software
Continuous capacities on continuous state spaces
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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This paper establishes a Stone-type duality between specifications and infLMPs. An infLMP is a probabilistic process whose transitions satisfy super-additivity instead of additivity. Interestingly, its simple structure can encode a mix of probabilistic and non-deterministic behavior, which, as we show, is strongly related to another well-known such model: probabilistic automata. Our duality puts in relation the category of infLMPs and a category of abstract representations of them based on properties only. We exhibit a Galois connection between these categories and show that we have an adjunct pair of functors when restricted to LMPs only. Our duality also shows that an infLMP can be considered as a demonic representative of a system's information. Moreover, it carries forward a view where states are less important, and events, or properties, become the main characters, as it should be in probability theory. Along the way, we show that bisimulation and simulation are naturally interpreted in this setting, and we exhibit the interesting relationship between infLMPs and the usual probabilistic modal logics. This paper is an extended version of a Concur '09 paper [13]; in particular, the comparison of infLMPs with probabilistic automata and the Galois connection are new.