Worst-case Reaction Time for Synchronous Programs : Studying the Tick Alignment Problem

Synchronous programs are ideally suited for the design of safety critical systems as they provide guarantees on determinism and deadlock freedom. In addition to such functional guarantees, guarantees on timing are also necessary. In this report, we study the problem of static worst case reaction time (WCRT) analysis of synchronous programs. While, there have been many recent attempts at studying this problem from the point of view of scalability and precision, one crucial aspect is yet to be examined from a fundamental viewpoint. Concurrent threads in a synchronous programs must align during every reaction, a problem that has been termed as the tick alignment problem (TAP), i.e., infeasible ticks that never align in practice must be ruled out for precision. We, for the first time, study TAP in the guise of a number theoretic formulation in order to not only explore its lower bound complexity, but also to develop heuristics that work well in practice. The developed algorithm that is based on the Maximum Weight Clique Problem. Extensive benchmarking reveals the relative superiority of the proposed approach. While being optimal it is also more efficient compared to one of the most efficient of known techniques, ILPC , which uses iterative approximation with integer linear programming techniques. Finally, using insights from the proposed TAP formulation, we develop a refinement of ILPC , called ILPCP , that excels in comparison to all known techniques for WCRT analysis.