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 P-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(n(1+epsilon)) time using m/n(epsilon) CREW PRAM processors, for any fixed epsilon < 1. This algorithm is analogous to 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 CREW PRAM processors. This algorithm is analogous to and nearly optimal with respect to the sequential algorithm of Paige and Tarjan.