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Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations

  • David de Frutos Escrig
  • Miguel Palomino
  • Ignacio Fábregas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5048)

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.

Keywords

Transition System Probabilistic System Natural Transformation Probabilistic Choice Common Framework 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© IFIP International Federation for Information Processing 2008

Authors and Affiliations

  • David de Frutos Escrig
    • 1
  • Miguel Palomino
    • 1
  • Ignacio Fábregas
    • 1
  1. 1.Departamento de Sistemas Informáticos y ComputaciónUniversidad Complutense de MadridSpain

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