Bisimulation through probabilistic testing
Information and Computation
Reactive, generative, and stratified models of probabilistic processes
Information and Computation
Bisimulation for probabilistic transition systems: a coalgebraic approach
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Probabilistic simulations for probabilistic processes
Nordic Journal of Computing
The Powerdomain of Indexed Valuations
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Nondeterminism and Probabilistic Choice: Obeying the Laws
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Category Theory and Computer Science
A hierarchy of probabilistic system types
Theoretical Computer Science - Selected papers of CMCS'03
Theoretical Computer Science - Selected papers of CMCS'03
Distributing probability over non-determinism
Mathematical Structures in Computer Science
New Bisimulation Semantics for Distributed Systems
FORTE '07 Proceedings of the 27th IFIP WG 6.1 international conference on Formal Techniques for Networked and Distributed Systems
RETRACTED: Semantic Domains for Combining Probability and Non-Determinism
Electronic Notes in Theoretical Computer Science (ENTCS)
Generic forward and backward simulations
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
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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 Fto another Gtransforms 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 Fthe equivalence induced by the epi-mono decomposition of the natural transformation relating Fand 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.