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A Coalgebraic Theory of Reactive Systems

Authors
Journal
Electronic Notes in Theoretical Computer Science
1571-0661
Publisher
Elsevier
Publication Date
Volume
209
Identifiers
DOI: 10.1016/j.entcs.2009.02.012
Keywords
  • Reactive Systems
  • Coalgebras
  • Labeled Transition Systems
Disciplines
  • Linguistics
  • Mathematics

Abstract

Abstract In this paper we investigate 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, the compositionality 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. Furthermore, if bisimilarity is compositional in the reactive system, then we can lift this coalgebra to a structured coalgebra.

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