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The Observational Power of Clocks \Lambda Rajeev Alur y Costas Courcoubetis z Thomas A. Henzinger x

Summary: The Observational Power of Clocks \Lambda
Rajeev Alur y Costas Courcoubetis z Thomas A. Henzinger x
We develop a theory of equivalences for timed systems. Two systems
are equivalent iff external observers cannot observe differences in their be­
havior. The notion of equivalence depends, therefore, on the distinguish­
ing power of the observers. The power of an observer to measure time
results in untimed, clock, and timed equivalences: an untimed observer
cannot measure the time difference between events; a clock observer uses
a clock to measure time differences with finite precision; a timed observer
is able to measure time differences with arbitrary precision.
We show that the distinguishing power of clock observers grows
with the number of observers, and approaches, in the limit, the distin­
guishing power of a timed observer. More precisely, given any equiva­
lence for untimed systems, two timed systems are k­clock congruent, for
a nonnegative integer k, iff their compositions with every environment
that uses k clocks are untimed equivalent. Both k­clock bisimulation con­
gruence and k­clock trace congruence form strict decidable hierarchies
that converge towards the corresponding timed equivalences. Moreover,
k­clock bisimulation congruence and k­clock trace congruence provide an


Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania
Henzinger, Thomas A. - Faculté Informatique et Communications, Ecole Polytechnique Fédérale de Lausanne


Collections: Computer Technologies and Information Sciences