The notions of bisimulation and simulation are used for graph reduction and are widely employed in many areas: modal logic, concurrency theory, set theory, formal verification, and so forth. In particular, in the context of formal verification they are used to tackle the so-called state-explosion problem. The faster algorithms to compute the maximum bisimulation on a given labeled graph are based on the crucial equivalence between maximum bisimulation and relational coarsest partition problem. As far as simulation is concerned, many algorithms have been proposed that turn out to be relatively inexpensive in terms of either time or space. In this paper we first revisit the state of the art about bisimulation and simulation, pointing out the analogies and differences between the two problems. Then, we propose a generalization of the relational coarsest partition problem, which is equivalent to the simulation problem. Finally, we present an algorithm that exploits such a characterization and improves on previously proposed algorithms for simulation.
