Coalgebraic Partition Refinement For All Functors.

Coalgebraic partition refinement generalizes classical transition system minimization to general system types equipped with a coalgebraic equivalence notion, subsuming strong, weighted, and probabilistic bisimilarity. The asymptotically fastest algorithm requires an ad-hoc condition on the system type and uses large amounts of memory, limiting the size of the transition system that can be handled. A subsequent distributed algorithm is able to handle larger systems by distributing the memory requirement over several compute nodes, but this algorithm is asymptotically slower. We present an algorithm that is applicable to all computable set functors, and runs in time O(k2n log n), where n is the number of states and k is the number of transitions per state. This algorithm is asymptotically slower than the fastest algorithm by a factor of k, but asymptotically faster than the distributed algorithm by a factor of n. In practice, our algorithm uses much less time and memory on existing benchmarks. Transition systems that previously required half an hour on HPC clusters can be minimized in seconds on a single core of a laptop by our algorithm. 2012 ACM Subject Classification Theory of computation