Computing Bisimulation-Based Comparisons

We provide the first algorithm with a polynomial time complexity, O((m + n)^2 n^2), for computing the largest bisimulation-based auto-comparison of a labeled graph in the setting with counting successors, where m is the number of edges and n is the number of vertices. This setting is like the case with graded modalities in modal logics and qualified number restrictions in description logics. Furthermore, by using the idea of Henzinger et al. for computing simulations, we give an efficient algorithm, with complexity O((m + n)n), for computing the largest bisimulation-based auto-comparison and the directed similarity relation of a labeled graph in the setting without counting successors. We also adapt our former algorithm for computing the simulation pre-order of a labeled graph in the setting with counting successors.