We define formally the notion of implementation for time critical syst
ems in terms of provability of properties described abstractly at the
specification level. We characterize this notion in terms of formulas
of the temporal logic TRIO and operational models of timed Petri nets,
and provide a method to prove that two given nets are in the implemen
tation relation. Refinement steps are often used as a means to derive
in a systematic way the system design starting from its abstract speci
fication. We present a method to formally prove the correctness of ref
inement rules for timed Petri nets and apply it to a few simple cases.
We show how the possibility to retain properties of the specification
in its implementation can simplify the verification of the designed s
ystems by performing incremental analysis at various levels of the spe
cification/implementation hierarchy. (C) 1998 - Elsevier Science B.V.
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