Validation of Mixed Signal-Alpha Real-Time Systems through A ne Calculus on Clock Synchronisation Constraints

In this paper we present the aane clock calculus as an extension of the formal veriication techniques provided by the Signal language. A Signal program describes a system of clock synchronisation constraints the consistency of which is veriied by compilation (clock calculus). Well-adapted in control-based system design, the clock calculus has to be extended in order to enable the validation of Signal-Alpha applications which usually contain important numerical calculations. The new aane clock calculus is based on the properties of aane relations induced between clocks by the reenement of Signal-Alpha speciications in a codesign context. AAne relations enable the derivation of a new set of synchronisability rules which represent conditions against which syn-chronisation constraints on clocks can be assessed. Properties of aane relations and synchronisability rules are derived in the semantical model of traces of Signal. A prototype implementing a subset of the synchro-nisability rules has been integrated in the Signal compiler and used for the validation of a video image coding application speciied using Signal and Alpha.