 
Summary: Computing Accumulated Delays in Realtime Systems \Lambda
Rajeev Alur y Costas Courcoubetis z Thomas A. Henzinger x
Abstract. We present a verification algorithm for duration properties of realtime
systems. While simple realtime properties constrain the total elapsed time between
events, duration properties constrain the accumulated satisfaction time of state pred
icates. We formalize the concept of durations by introducing duration measures for
timed automata. A duration measure assigns to each finite run of a timed automaton
a real number the duration of the run which may be the accumulated satisfaction
time of a state predicate along the run. Given a timed automaton with a duration
measure, an initial and a final state, and an arithmetic constraint, the durationbounded
reachability problem asks if there is a run of the automaton from the initial state to
the final state such that the duration of the run satisfies the constraint. Our main
result is an (optimal) Pspace decision procedure for the durationbounded reachability
problem.
1 Introduction
Over the past decade, model checking [CE81, QS81] has emerged as a powerful tool for the automatic
verification of finitestate systems. Recently the modelchecking paradigm has been extended to
realtime systems [ACD93, HNSY94, AFH96]. Thus, given the description of a finitestate system
together with its timing assumptions, there are algorithms that test whether the system satisfies
a specification written in a realtime temporal logic. A typical property that can be specified in
