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Ready Simulation, Bisimulation, and the Semantics of CCSLike Languages
, 1993
"... The questions of program comparison  asking when two programs are equal, or when one is a suitable substitute for another  are central in the semantics and verification of programs. It is not obvious what the definitions of comparison should be for parallel programs, even in the relatively sim ..."
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The questions of program comparison  asking when two programs are equal, or when one is a suitable substitute for another  are central in the semantics and verification of programs. It is not obvious what the definitions of comparison should be for parallel programs, even in the relatively simple case of core languages for concurrency, such as the kernel language of Milner's CCS. We introduce some criteria for judging notions of program comparison. Our basic notion is that of a congruence: two programs are equivalent with respect to a language L and a set of observations O iff they cannot be distinguished by any observation in O in any context of L. Bisimulation, the notion of program equivalence ordinarily used with CCS, is finer than CCS congruence: there are two programs which are not bisimilar, but cannot be told apart by CCS contexts. We explore the possibility of making bisimulation into a congruence. We CCS is defined by a set of structured operational rules. We introduc...
Terminal Metric Spaces of Finitely Branching and Image Finite Linear processes
, 1997
"... Wellknown metric spaces for modelling finitely branching and image finite systems are shown to be (the carrier of) terminal coalgebras. Introduction In the area of metric semantics, various metric structures have been proposed to model a wide spectrum of programming notions (see, e.g., [BV96]). In ..."
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Wellknown metric spaces for modelling finitely branching and image finite systems are shown to be (the carrier of) terminal coalgebras. Introduction In the area of metric semantics, various metric structures have been proposed to model a wide spectrum of programming notions (see, e.g., [BV96]). In this paper, we focus on metric structures for modelling nondeterministic systems which may give rise to both terminating and nonterminating computations. The systems we have in mind are labelled transition systems [Kel76]. A large variety of programming notions can be modelled by means of these systems (see, e.g., [Plo81]). The models we consider are linear (cf. [Pnu85]). In these models, the locations in a computation where a nondeterministic choice is made are not visible. These linear models are usually contrasted with branching models (cf. [Gla90]). In those models, the positions in the computation where a nondeterministic choice is made are administrated. Typical examples of linear me...
De BakkerZucker Processes Revisited
 Information and Computation
, 1999
"... The sets of compact and of closed subsets of a metric space endowed with the Hausdorff metric are studied. Both give rise to a functor on the category of 1bounded metric spaces and nonexpansive functions. It is shown that the former functor has a terminal coalgebra and that the latter does not. ..."
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The sets of compact and of closed subsets of a metric space endowed with the Hausdorff metric are studied. Both give rise to a functor on the category of 1bounded metric spaces and nonexpansive functions. It is shown that the former functor has a terminal coalgebra and that the latter does not. Introduction In the seventies, the use of trees was quite popular in denotational semantics of programming languages. Infinite computations were modelled by infinite trees. These infinite trees were obtained by providing the set of finite trees with an order and by completing the ordered space. In the late seventies, Maurice Nivat defined a distance function on finite trees. When this distance function turned out to be a metric, even an ultrametric, the following question arose naturally: How are the completed ordered space of finite trees and the completed metric space of finite trees related? It turned out that the latter is the set of maximal elements of the former. This result may be se...