A Domain View of Timed Behaviors ? Roman Dubtsov 1 , Elena Oshevskaya 2 , and Irina Virbitskaite 2 1 Institute of Informatics System SB RAS, 6, Acad. Lavrentiev av., 630090, Novosibirsk, Russia; 2 Institute of Mathematics SB RAS, 4, Acad. Koptyug av., 630090, Novosibirsk, Russia; dubtsov,eso,virb@iis.nsk.su Abstract. The intention of this paper is to introduce a timed extension of transition systems with independence, and to study its categorical interrelations with other timed ”true-concurrent” models. In particular, we show the existence of a chain of coreflections leading from a category of the model of timed transition systems with independence to a category of a specially defined model of marked Scott domains. As an intermediate semantics we use a model of timed event structures, able to properly capture causality, conflict, and concurrency among events which arise in the presence of time delays of the events. 1 Introduction The behaviour of concurrent systems is often specified in terms of states and transitions between states, the labels on the transitions represent the observable part of system’s behaviour. The simplest formal model of computation able to express naturally this idea is that of labelled transition systems. However, they are a representative of the interleaving approach to concurrency and hence do not allow one to draw a natural distinction between interleaved and concurrent executions of system’s actions. Two most popular ”true concurrent” extensions of transition systems, aiming to overcome limitations of the interleaving approach, are asynchronous transition systems, introduced independently by Bednarczyk [1] and Shields [2], and transitions systems with independence, proposed by Winskel and Nielsen [3]. Category theory [4] has been successfully exploited to structure the tangled world of models for concurrency. Within this framework, objects of categories represent processes and morphisms correspond to behavioural relations between the processes, i.e. to simulations. The category-theoretic approach allows for natural formalization of the fact that one model is more expressive than another in terms of an ”embedding”, most often taking the form of a coreflection, i.e. an adjunction in which the unit is an isomorphism. For example, Hildenbrandt and ? The second author is supported in part by the RFBR (grant 12-01-00873-a), by the President Program ”Leading Scientific Schools” (grant NSh-7256.2010.1), and by the Federal Program ”Research and educational personnel for innovative Russia” (grant 8206).