The Complexity of Bisimulation and Simulation on Finite Systems
Abstract
In this paper the computational complexity of the (bi)simulation problem over restricted graph classes is studied. For trees given as pointer structures or terms the (bi)simulation problem is complete for logarithmic space or NC1, respectively. This solves an open problem from Balc\'azar, Gabarr\'o, and S\'antha. Furthermore, if only one of the input graphs is required to be a tree, the bisimulation (simulation) problem is contained in AC1 (LogCFL). In contrast, it is also shown that the simulation problem is P-complete already for graphs of bounded path-width.
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