Semantics and verification of action diagrams with linear timing

Abstract

Specifications containing linear timing constraints, such as found in action diagrams (timing diagrams) defining interface behaviors, are often used in practice. Although efficient O(n 3 ) shortest path algorithms exist for computing the minimum and maximum time distances between actions, subject to the timing constraints, there is so far no accurate method that can decide (a) whether a specification of this kind is realizable (i.e., can be simulated by a causal system), and (b) given the action diagrams of the interfaces of two or more communicating systems, whether the systems implementing such independent specifications will correctly interoperate (i.e., satisfy the respective protocols and timing assumptions). First we illustrate the weakness of existing action diagram verification techniques: the causality issue is not addressed, and the proposed methods to answer the compatibility (interoperability) question yield false negative answers in many practical situations. We then define the meaning of causality in an action diagram specification and state a set of sufficient conditions for causality to hold. This development then leads to an exact procedure for the verification of the interface compatibility of communicating action diagrams. the results are illustrated on a practical example.