Syntax-driven Behavior Partitioning for Model-checking of Esterel Programs

We consider the issue of exploiting the structural form of Esterel programs to partition the algorithmic RSS (reachable state space) fix-point construction used in model-checking techniques. The basic idea sounds utterly simple, as seen on the case of sequential composition: in P; Q, first compute entirely the states reached in P, and then only carry on to Q, each time using only the relevant transition relation part. Here a brute-force symbolic breadth-first search would have mixed the exploration of P and Q instead, in case P had different behaviors of various lengths, and that would result in irregular BBD representation of temporary state spaces, a major cause of complexity in symbolic model-checking.Difficulties appear in our decomposition approach when scheduling the different transition parts in presence of parallelism and local signal exchanges. Program blocks (or “Macro-states”) put in parallel can be synchronized in various ways, due to dynamic behaviors, and considering all possibilities may lead to an excessive division complexity. The goal is here to find a satisfactory trade-off between compositional and global approaches. Concretely we use some of the features of the TiGeR BDD library, and heuristic orderings between internal signals, to have the transition relation progress through the program behaviors to get the same effect as a global RSS computation, but with much more localized transition applications. We provide concrete benchmarks showing the usefulness of the approach.