Abstract
Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with n labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game, called simulation game. We offer the first conditional lower bounds for this problem, and we relate its complexity (for computation, verification, and certification) to some variants of n × n matrix multiplication. We show that any O(nα)-time algorithm for simulation games, even restricting to acyclic games/structures, can be used to compute n × n boolean matrix multiplication (BMM) in O(nα) time. In the acyclic case, we match this bound by presenting the first subcubic algorithm, based on fast BMM, and running in nω+o(1) time (where ω
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