# A linear parallel algorithm to compute bisimulation and relational coarsest partitions

The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access machines (PRAMs). More precisely, with n states, m transitions and |π΄ππ‘|β€ m action labels, we provide an algorithm on max(n,m) processors that calculates strong bisimulation in time O(n+|π΄ππ‘|) and space O(n+m). The best-known PRAM algorithm has time complexity O(nlog n) on a smaller number of processors making it less suitable for massive parallel devices such as GPUs. An implementation on a GPU shows that the linear time-bound is achievable on contemporary hardware.

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