Computing Bisimulation-Based Comparisons

By using the idea of Henzinger et al. for computing the similarity relation, we give an efficient algorithm, with complexity O((m + n)n), for computing the largest bisimulation-based autocomparison and the directed similarity relation of a labeled graph for the setting without counting successors, where m is the number of edges and n is the number of vertices. Moreover, we provide the first algorithm with a polynomial time complexity, O((m + n)n), for computing such relations but for the setting with counting successors (like the case with graded modalities in modal logics and qualified number restrictions in description logics).