A linear parallel algorithm to compute bisimulation and relational coarsest partitions

by   Jan Martens, et al.

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 |𝐴𝑐𝑑|≀ m action labels, we provide an algorithm on max(n,m) processors that calculates strong bisimulation in time O(n+|𝐴𝑐𝑑|) 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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