Reducing Time and/or Memory Consumption of the SOG Construction in a Parallel Context

Abstract

An efficient way to cope with the combinatorial explosion problem induced by the model checking process is to compute the Symbolic Observation Graph (SOG). Such a graph is a condensed representation of the state space that is obtained by taking advantage of symbolic representation of the nodes. Each node, called aggregate, represents a set of explicit states and is encoded using Multi-valued decision diagrams. In a previous work, we have shown that parallel and distributed approaches can improve drastically the performances of the SOG computation regarding a sequential construction. In this paper, we go a step forward in improving the SOG construction process by reducing, on the fly, the size of its aggregates. We propose a Multi-valued decision diagrams (MDDs) based algorithm to determine a single representative for each strongly connected component in every aggregate allowing to remove from memory a consequent number of states which are no more necessary for the construction process. Two parallel approaches for the building of an SOG are proposed using such an optimization. The first approach is based on a shared memory architecture, while the second is based on a distributed memory one. The results of our preliminary experiments show that, in first case, the canonization allows to obtain more compact SOG (in terms of memory consumption) while increasing the computation time. However, for the distributed memory based approach, the canonization allows to reduce the size of exchanged messages and therefore reducing communication time.