Abstract
Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic distributions functors with the multiset functor by means of adequate natural transformations. This leads us to the general topic that we investigate in the paper: a natural transformation from a functor F to another G transforms F-bisimulations into G-bisimulations but, in general, it is not possible to express G-bisimulations in terms of F-bisimulations. However, they can be characterized by considering Hughes and Jacobs’ notion of simulation, taking as the order on the functor F the equivalence induced by the epi-mono decomposition of the natural transformation relating F and G. We also consider the case of alternating probabilistic systems where non-deterministic and probabilistic choices are mixed, although only in a partial way, and extend all these results to categorical simulations.
Research supported by the Spanish projects DESAFIOS TIN2006-15660-C02-01, WEST TIN2006-15578-C02-01 and PROMESAS S-0505/TIC/0407.
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de Frutos Escrig, D., Palomino, M., Fábregas, I. (2008). Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations. In: Suzuki, K., Higashino, T., Yasumoto, K., El-Fakih, K. (eds) Formal Techniques for Networked and Distributed Systems – FORTE 2008. FORTE 2008. Lecture Notes in Computer Science, vol 5048. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68855-6_18
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DOI: https://doi.org/10.1007/978-3-540-68855-6_18
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