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