Abstract
We present a study of the notion of coalgebraic simulation introduced by Hughes and Jacobs. Although in their original paper they allow any functorial order in their definition of coalgebraic simulation, for the simulation relations to have good properties they focus their attention on functors with orders which are strongly stable. This guarantees a so-called “composition-preserving” property from which all the desired good properties follow. We have noticed that the notion of strong stability not only ensures such good properties but also “distinguishes the direction” of the simulation. For example, the classic notion of simulation for labeled transition systems, the relation “p is simulated by q”, can be defined as a coalgebraic simulation relation by means of a strongly stable order, whereas the opposite relation, “p simulates q”, cannot. Our study was motivated by some interesting classes of simulations that illustrate the application of these results: covariant-contravariant simulations and conformance simulations.
Research supported by the Spanish projects DESAFIOS TIN2006-15660-C02-01, WEST TIN2006-15578-C02-01, PROMESAS S-0505/TIC/0407 and UCM-BSCH GR58/08/910606.
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Fábregas, I., de Frutos Escrig, D., Palomino, M. (2009). Non-strongly Stable Orders Also Define Interesting Simulation Relations. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds) Algebra and Coalgebra in Computer Science. CALCO 2009. Lecture Notes in Computer Science, vol 5728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03741-2_16
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DOI: https://doi.org/10.1007/978-3-642-03741-2_16
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