2005
DOI: 10.1007/11548133_20
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A Categorical Approach to Simulations

Abstract: Abstract. Simulations are a very natural way of relating concurrent systems, which are mathematically modeled by Kripke structures. The range of available notions of simulations makes it very natural to adopt a categorical viewpoint in which Kripke structures become the objects of several categories while the morphisms are obtained from the corresponding notion of simulation. Here we define in detail several of those categories, collect them together in various institutions, and study their most interesting pr… Show more

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Cited by 5 publications
(4 citation statements)
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“…We have introduced several concepts of simulations and shown some basic results about them; M. Palomino's PhD thesis [29] (in Spanish) deals with this subject in more detail, also covering: equational abstractions, simulations of protocols, algebraic simulations in rewriting logic, and categories of Kripke structures and simulations. Related conference papers in English include [22,26,30]. The study of simulations in the presence of strategies is work in progress.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…We have introduced several concepts of simulations and shown some basic results about them; M. Palomino's PhD thesis [29] (in Spanish) deals with this subject in more detail, also covering: equational abstractions, simulations of protocols, algebraic simulations in rewriting logic, and categories of Kripke structures and simulations. Related conference papers in English include [22,26,30]. The study of simulations in the presence of strategies is work in progress.…”
Section: Discussionmentioning
confidence: 99%
“…The notion of simulation is appropriate for this, but we notice that the mismatch in atomicity requires the additional flexibility provided by the notion of stuttering simulation, that we also introduced in the context of rewriting logic in previous conference papers [22,30]. Here we use this concept to show that a stack machine correctly implements the operational semantics of a functional language.…”
Section: Introductionmentioning
confidence: 93%
“…The general idea is to use algebraic and/or rewriting logic methods to define such an H as either a function or a relation. Another idea explored in depth in [332,377] is that simulations and stuttering simulations are arrows in appropriate categories, so that they can be composed, i.e., the entire approach is compositional, so that we can combine several of the above-mentioned abstraction methods to arrive at the desired abstraction. A general emphasis common to all the abstraction methods presented in [192,302,331,332] is on the inductive proof obligations that need to be discharged in order to prove that the proposed simulation H is correct.…”
Section: Simulation and Abstractionmentioning
confidence: 99%
“…The institution of [12] resembles our local institution and uses lts's as models, but its logic contains also first-order constructs. An institution for CTL * and Kripke structures is given in [18]. Institutions aside, our local logic is related to other actionbased variants of CTL or CTL * , such as ACTL* ( [19]).…”
Section: Related Workmentioning
confidence: 99%