Checking coverage for infinite collections of timed scenarios

We consider message sequence charts enriched with timing constraints between pairs of events. As in the untimed setting, an infinite family of time-constrained message sequence charts (TC-MSCs) is generated using an HMSC—a finite-state automaton whose nodes are labelled by TC-MSCs. A timed MSC is an MSC in which each event is assigned an explicit time-stamp. A timed MSC covers a TC-MSC if it satisfies all the time constraints of the TC-MSC. A natural recognizer for timed MSCs is a message-passing automaton (MPA) augmented with clocks. The question we address is the following: given a timed system specified as a time-constrained HMSC H and an implementation in the form of a timed MPA А, is every TC-MSC generated by H covered by some timed MSC recognized by А? We give a complete solution for locally synchronized time-constrained HMSCs, whose underlying behaviour is always regular. We also describe a restricted solution for the general case