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Computer Science > Logic in Computer Science

arXiv:2402.00963 (cs)
[Submitted on 1 Feb 2024]

Title:Non-strongly Stable Orders Also Define Interesting Simulation Relations

Authors:Ignacio Fábregas, David de Frutos-Escrig, Miguel Palomino
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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.
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:2402.00963 [cs.LO]
  (or arXiv:2402.00963v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2402.00963
Journal reference: Algebra and Coalgebra in Computer Science (CALCO) 2009. Lecture Notes in Computer Science, 5728. Springer
Related DOI: https://doi.org/10.1007/978-3-642-03741-2%5C_16

Submission history

From: Ignacio Fábregas [view email]
[v1] Thu, 1 Feb 2024 19:29:46 UTC (16 KB)
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