The 2006 International Arab Conference on Information Technology (ACIT'2006)      Djamel Eddine Saïdouni and Nabil Belala LIRE Laboratory, University of Mentouri, 25000 Constantine, Algeria saidounid@hotmail.com , nbelala@gmail.com  This paper introduces a realtime model based on a trueconcurrency semantics, expressing parallel behaviors and supporting at the same time timing constraints, explicit actions durations, structural and temporal nonatomicity of actions and urgency. This model is called Durational Action Timed Automata*. As an application, we propose translating rules from D LOTOS language specifications to DATA*'s structures.  Realtime systems, Actions duration, Maximalitybased semantics, DATA*’s   Specification of real*time systems is a quite difficult process since these systems are known to be complex and critical. Formal models are usually used to specify behaviors and verify some expected properties; one can cite timed extensions of Petri nets [24,26], process algebras as TCCS, ET*LOTOS, RT*LOTOS, D*LOTOS [14,15,21,25,31] and state*transition models like timed automata [1,2] which extend state*transition graphs with timing constraints using a set of real*valued clocks. In this context, many questions have been raised and studied in the literature; an important one is how to give semantics to a specification model to be able to express concurrent and parallel behaviors in a natural way, i.e. to distinguish between sequential and parallel runs of actions. This is not the case of the interleaving semantics: to use this latter advisedly, actions must be temporally and structurally atomic (actions are indivisible and of null duration). Another question concerns the expression of non* null duration actions. To do this, most of works consider actions as two instantaneous events: their start and their completion, in addition to the wait between these events. Although this approach seems to be attractive, it may contribute toward graph explosion in state*transition models. Timed automata model and most of their sub*classes and extensions opt for splitting actions up into start and completion events. Among timed automata sub*classes, we can quote Timed Safety Automata [20] in which a state of an automaton can contain local timing clock constraint called invariant, EventRecording Automata [3] in which a corresponding clock x a is reset automatically with each occurrence of an action a, Dynamic Timed Automata [13,22] including a set of clocks no longer global in all the system but local in each automaton state, Timed Automata with Deadlines of [8,9] allowing the expression of urgency at the level of transitions by a left*closed deadline constraints, and Updatable Timed Automata [10,11,12] which are more expressive than original timed automata and allow, besides clock reset, assigning non*null values to clocks. By taking these models in consideration, we will show some points that may lead to difficulties in expressing non*null duration actions as well as concurrent and parallel behaviors. The first is certainly splitting actions up into start and completion events that is inherent to these models. To get round the posed problem of graph explosion, an alternative consists in representing actions of non*null duration as non* instantaneous transitions, following the example of timed automata with noninstantaneous actions model [4]. According to the semantics of this latter, transitions are indivisible requiring that actions are structurally atomic, which prevents the execution of parallel actions. To observe clearly, consider the example of a process P executing two concurrent actions a and b. If the respective durations of a and b are 10 and 12 units of time, the underlying behavior can be expressed, as shown in Figure 1, by respectively a labeled transitions system, a timed automaton or a timed automaton with non*instantaneous actions. a↑ and a↓ express respectively the start and the completion of an action a. When actions a and b are of non*null duration, their simultaneous execution is included implicitly in the state s in the timed automaton of Figure 1.(b). This information is lost in Figure 1.(c) because of structural atomicity of actions. (c) a↑, x:=0 b↑, y :=0 a↑, x:=0 a↓, x =10? a↑, x:=0 b↓, y =12? a↓, x =10? b↑, y :=0 b↓, y =12? a↓, x =10? b↑, y :=0 b a a b P P (a) (b) true, { x} , a, x= 10, { } P true, { y} , b, y= 12, { } true, { x} , a, x= 10, { } true, { y} , b, y= 12, { } s Figure 1: Concurrent actions a and b.