Istituto di Scienza e Tecnologie dell'Informazione     
Ciancia V. Interaction and observation: categorical semantics of reactive systems trough dialgebras. In: CALCO 2013 - 5th Conference on Algebra and Coalgebra in Computer Science. 5th International Conference (Warsaw, Poland, 3-6 November 2013). Proceedings, pp. 110 - 125. Reiko Heckel, Stefan Milius (eds.). (Lecture Notes in Computer Science, vol. 8089). Springer, 2013.
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is built-in, and semantic equivalence arises from it, instead of being determined by a (possibly difficult) understanding of the side effects of a component in isolation. Behavioural equivalence in dialgebras is determined by how a given process interacts with the others, and the obtained observations. We develop a technique to inter-define categories of dialgebras of different functors, that in particular permits us to compare a standard coalgebraic semantics and its dialgebraic counterpart. We exemplify the framework using the CCS and the π-calculus. Remarkably, the dialgebra giving semantics to the π-calculus does not require the use of presheaf categories.
URL: http://link.springer.com/chapter/10.1007%2F978-3-642-40206-7_10
DOI: 10.1007/978-3-642-40206-7_10
Subject Semantics
Interactive Systems
Category theory
D.3.1 Formal Definitions and Theory
F.1.2 Modes of Computation

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