Non-strongly Stable Orders Also Define Interesting Simulation Relations

Abstract

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.

On the specification of modal systems: A comparison of three frameworks

“…For MTS and refinement we refer the reader to, e.g., [7,17,18] for motivation and examples, whereas [9,10] can be consulted for more information regarding covariant-contravariant simulations.…”

Similarity Quotients as Final Coalgebras

“…More recently [2,4,7,11,12,19] there have been several coalgebraic studies of simulation, in which the final F -coalgebra carries a preorder. This is valuable for someone who wants to study bisimilarity and similarity together: equality represents bisimilarity, and the preorder represents similarity.…”

Logics for Contravariant Simulations

“…This leads to two new notions of simulation: covariant-contravariant simulation and conformance simulation, that we roughly sketched in [6] and presented in detail in [7], where we proved that they can be obtained as particular instances of the general notion of categorical simulation developed by Hughes and Jacobs [9].…”

“…We say that the LTS is finitary when for each p ∈ P and a ∈ A we have |{p | p a −→ p }| < ∞. We refer to [7] for a more extensive motivation of covariant-contravariant simulations; here we only comment on the case of input/output automata. To define an adequate simulation notion for them we observe that the classic approach to simulations is based on the definition of semantics for reactive systems, where all the actions of the processes correspond to input actions that the user must trigger.…”

“…After showing in [7] that they can be formalized as categorical simulations, in this paper we present their logical characterizations. We expect that they will contribute to clarify the meaning of the corresponding simulations, shedding light on the properties that can be established when using these two frameworks within a specification procedure.…”