A Multi-Core Solver for Parity Games

We describe a parallel algorithm for solving parity games,\ud with applications in, e.g., modal mu-calculus model\ud checking with arbitrary alternations, and (branching) bisimulation\ud checking. The algorithm is based on Jurdzinski's Small Progress\ud Measures. Actually, this is a class of algorithms, depending on\ud a selection heuristics.\ud \ud Our algorithm operates lock-free, and mostly wait-free (except for\ud infrequent termination detection), and thus allows maximum\ud parallelism. Additionally, we conserve memory by avoiding storage\ud of predecessor edges for the parity graph through strictly\ud forward-looking heuristics.\ud \ud We evaluate our multi-core implementation's behaviour on parity games\ud obtained from mu-calculus model checking problems for a set of\ud communication protocols, randomly generated problem instances, and\ud parametric problem instances from the literature.\ud \u

Distributed Local Resolution of Boolean Equation Systems

Boolean Equation Systems (BESs) allow to represent various problems encountered in the area of propositional logic programming and verification of concurrent systems. Several sequential algorithms for global and local BES resolution have been proposed so far, mainly in the field of verification; however, these algorithms do not scale up satisfactorily as the size of BESs increases. In this paper, we propose a distributed algorithm, called DSOLVE, which performs the local resolution of a BES using a set of machines connected by a network. Our experiments for solving large BESs using clusters of PCs show linear speedups and a scalable behaviour of DSOLVE w.r.t. its sequential counterpart. 1