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Coalgebras and Compositionality

Corina Cirstea Department of Electronics and Computer Science University of Southampton 2pm 4 June 2004 Room 6324, JCMB, King's Buildings

In the modelling of state-based systems as coalgebras, the emphasis is on the observable system behaviour, with the notion of coalgebraic bisimulation providing a uniform way to define an observational equivalence relation between system states. In addition, the (weaker) notion of coalgebraic simulation allows various kinds of refinement relations between system states to also be modelled coalgebraically.

The coalgebraic approach is intrinsically compositional with respect to system types, in that system combinations can be modelled at the level of coalgebraic signatures using operations such as functor composition, product or coproduct. In this talk, I will show that this compositionality can be lifted to defining (a) notions of simulation for combined systems, and (b) logics which characterise bisimulation, or specific notions of simulation, on combined systems. These results can be applied to derive notions of simulation, as well as expressive logics, for a large class of probabilistic systems.

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