Bisimulation by Partitioning Is Ω((m+n) logn)

An asymptotic lowerbound of Ω((m+n)logn) is established for partition refinement algorithms that decide bisimilarity on labeled transition systems. The lowerbound is obtained by subsequently analysing two families of deterministic transition systems - one with a growing action set and another with a fixed action set. For deterministic transition systems with a one-letter action set, bisimilarity can be decided with fundamentally different techniques than partition refinement. In particular, Paige, Tarjan, and Bonic give a linear algorithm for this specific situation. We show, exploiting the concept of an oracle, that the approach of Paige, Tarjan, and Bonic is not of help to develop a generic algorithm for deciding bisimilarity on labeled transition systems that is faster than the established lowerbound of Ω((m+n)logn).