Bérard Serge Haddad Interrupt Timed Automata : A Step Further Research Report LSV - 09 - 01 January 2009

In this work, we introduce the class of Interrupt Timed Automata (ITA), which are well suited to the description of multi-task systems with interruptions in a single processor environment. This model is a subclass of hybrid automata. While reachability is undecidable for hybrid automata we show that in ITA the reachability problem is decidable. More precisely we show that the untimed language of an ITA is effectively regular via a generalized class graph. We establish that the reachability problem for ITA is in 2-NEXPTIME and in NP when the number of clocks is fixed. To prove the results on reachability, we first consider a subclass ITA− which still describes usual interrupt systems and for which the reachability problem is in NEXPTIME and in NP when the number of clocks is fixed (without any class graph). Then we prove that any ITA can be reduced to an equivalent ITA− w.r.t. the language equivalence. Additionally we show that the languages of ITA are neither closed under complementation nor under intersection. We also compare the expressive power of TA and ITA and prove that the corresponding families of languages are incomparable. The result also holds for languages accepted by controlled real-time automata (CRTA), another extension of timed automata. So, we finally combine ITA with CRTA in a model which encompasses both classes and show that the reachability problem is still decidable.