Distributed Computation of Fixed Points on Dependency Graphs

Dependency graph is an abstract mathematical structure for representing complex causal dependencies among its vertices. Several equivalence and model checking questions, boolean equation systems and other problems can be reduced to fixed-point computations on dependency graphs. We develop a novel distributed algorithm for computing such fixed points, prove its correctness and provide an efficient, open-source implementation of the algorithm. The algorithm works in an on-the-fly manner, eliminating the need to generate a priori the entire dependency graph. We evaluate the applicability of our approach by a number of experiments that verify weak simulation/bisimulation equivalences between CCS processes and we compare the performance with the well-known CWB tool. Even though the fixed-point computation, being a P-complete problem, is difficult to parallelize in theory, we achieve significant speed-ups in the performance as demonstrated on a Linux cluster with several hundreds of cores.