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00925njm 22002777a 4500 dc Fábregas Alfaro, Ignacio author Frutos Escrig, David De author Palomino Tarjuelo, Miguel author 2009 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. Fábregas Alfaro, I., Frutos Escrig, D. & Palomino Tarjuelo, M. «Non-strongly Stable Orders Also Define Interesting Simulation Relations». Algebra and Coalgebra in Computer Science, editado por Alexander Kurz et al., vol. 5728, Springer Berlin Heidelberg, 2009, pp. 221-35. DOI.org (Crossref), https://doi.org/10.1007/978-3-642-03741-2_16. 978-3-642-03740-5 10.1007/978-3-642-03741-2_16 https://hdl.handle.net/20.500.14352/53215 https//doi.org/10.1007/978-3-642-03741-2_16 http://link.springer.com/content/pdf/10.1007%2F978-3-642-03741-2_16 Non-strongly stable orders also define interesting simulation relations