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Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations

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Frutos Escrig, David de and Palomino, Miguel and Fábregas, Ignacio (2008) Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations. In Formal Techniques for Networked and Distributed Systems – FORTE 2008 : 28th IFIP WG 6.1 International Conference Tokyo, Japan, June 10-13, 2008 Proceedings. Lecture notes in computer science (5048). Springer, pp. 283-298. ISBN 978-3-540-68854-9

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Official URL: http://link.springer.com/content/pdf/10.1007%2F978-3-540-68855-6_18


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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.


Item Type:Book Section
Subjects:Sciences > Computer science
ID Code:20747
Deposited On:10 Apr 2013 10:55
Last Modified:10 Aug 2018 08:29

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