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Timed Delay Bisimulation is an Equivalence Relation for Timed Transition Systems

100%

Gribovskaya N. , Virbitskaite I.

Fundamenta Informaticae

2009

tom Vol. 93, nr 1-3

127-142

Timed transition systems are a widely studied model for real-time systems. The intention of the paper is to show the applicability of the general categorical framework of openmaps in order to prove that timed delay equivalence is indeed an equivalence relation in the setting of timed transition systems with invariants. In particular, we define a category of the model under consideration and an accompanying (sub)category of observations to which the corresponding notion of open maps is developed. We then use the open maps framework to obtain an abstract equivalence relation which is established to coincide with timed delay bisimulation.

Open Maps and Observational Equivalences for Timed Partial Order Models

100%

Virbitskaite I. B. , Gribovskaya N. S.

Fundamenta Informaticae

2004

tom Vol. 60, nr 1-4

383--399

The intention of the paper is to show the applicability of the general categorical framework of open maps to the setting of timed extensions of partial order models, in order to transfer general concepts of equivalences to the models. In particular, we define categories of timed event structures, whose morphisms are to be thought of as simulations, and accompanying (sub)categories of observations, to which the corresponding notions of open maps are developed. We then use the open maps framework to obtain abstract bisimilarities which are established to coincide with timed extensions of well-known partial order based equivalences.

On open maps of Borel sets

75%

Ostrovsky A. V.

Fundamenta Mathematicae

1994-1995

tom 146

nr 3

203-213

We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not $G_δ · F_σ$ and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.