\title{Timed Automata with non-Instantaneous Actions}

\author{Roberto Barbuti \and Nicoletta De Francesco \and Luca Tesei}

\begin{abstract} 
In this paper we propose a model, {\em timed automata with
non-instantaneous actions}, which allows representing in a suitable
way real-time systems.  Timed automata with non-instantaneous actions
extend the timed automata model by dropping the assumption that
actions are instantaneous: in our model an action can take some time
to be completed.  We investigate the expressiveness of the new model,
comparing it with classical timed automata.  In particular, we study
the set of timed languages which can be accepted by timed automata
with non-instantaneous actions.  We prove that timed automata with
non-instantaneous actions are more expressive than timed automata and
less expressive than timed automata with $\epsilon$ edges.  Moreover
we define the parallel composition of timed automata with
non-instantaneous actions.  We point out how the specification by
means of a parallel timed automaton with non-instantaneous actions is,
in some cases, more convenient to represent reality.  
\end{abstract}

\begin{keywords} real-time systems, timed automata, timed languages.
\end{keywords}