 
Summary: Timed Automata
Rajeev Alur ?
Abstract. Model checking is emerging as a practical tool for automated debugging
of complex reactive systems such as embedded controllers and network protocols (see
[23] for a survey). Traditional techniques for model checking do not admit an explicit
modeling of time, and are thus, unsuitable for analysis of realtime systems whose
correctness depends on relative magnitudes of different delays. Consequently, timed
automata [7] were introduced as a formal notation to model the behavior of realtime
systems. Its definition provides a simple way to annotate statetransition graphs with
timing constraints using finitely many realvalued clock variables. Automated analysis
of timed automata relies on the construction of a finite quotient of the infinite space of
clock valuations. Over the years, the formalism has been extensively studied leading
to many results establishing connections to circuits and logic, and much progress has
been made in developing verification algorithms, heuristics, and tools. This paper
provides a survey of the theory of timed automata, and their role in specification and
verification of realtime systems.
1 Modeling
Transition systems. We model discrete systems by statetransition graphs whose transi
tions are labeled with event symbols. A transition system S is a tuple hQ; Q 0 ; \Sigma ; !i, where
Q is a set of states, Q 0 ` Q is a set of initial states, \Sigma is a set of labels (or events), and
