Parallel Algorithms for Relational Coarsest Partition Problems

Relational Coarsest Partition Problems (RCPPs) play a vital role in verifying concurrent systems. It is known that RCPPS are Ρ-complete and hence it may not be possible to design polylog time parallel algorithms for these problems. In this paper, we present two efficient parallel algorithms for RCPP, in which its associated label transition system is assumed to have m transitions and n states. The first algorithm runs in O(n1+∈) time using m/n∈ CREW PRAAM processors, for any fixed ∈ < 1. This algorithm is analogous and optimal with respect to the sequential algorithm of Kanellakis and Smolka. The second algorithm runs in O(n log n) time using m/n log n CREW PRAM processor. This algorithm is analogous and nearly optimal with respect to the sequential algorithm of Paige and Tarjan.