A Coalgebraic Theory of Reactive Systems

Bonchi, Filippo and Montanari, Ugo (2006) A Coalgebraic Theory of Reactive Systems. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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Abstract

In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, under rather restrictive conditions, thecompositionality of the abstract semantics (bisimilarity). Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., as the unique morphism to the final coalgebra. Moreover, if lifting a coalgebra to a structured setting is possible, then bisimilarity is compositional with respect to the lifted structure. Here we show that for every reactive system we can build a coalgebra. Further, if bisimilarity is compositional in the reactive system, then we can lift this coalgebra to a structured coalgebra.

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