From Petri Nets with Shared Variables to ITL

Petri nets and Interval Temporal Logic (ITL) are two formalisms for the specification and analysis of concurrent computing systems. Petri nets allow for a direct expression of causality aspects in system behaviour and in particular support system verification based on partial order reductions or invariant-based techniques. ITL, on the other hand, supports system verification by proving that the formula describing a system implies the formula describing a correctness requirement. It would therefore be desirable to establish a strong semantical link between these two models, thus allowing one to apply diverse analytical methods and techniques to a given system design. We have recently proposed such a semantical link between the propositional version of ITL (PITL) and Box Algebra (BA), which is a compositional model of basic (low-level) Petri nets supporting handshake action synchronisation between concurrent processes. In this paper, we extend this result by considering a compositional model of (high-level) Petri nets where concurrent processes communicate through shared variables. The main result is a method for translating a design expressed using a high-level Petri net into a semantically equivalent ITL formula.