Saving Space in a Time Efficient Simulation Algorithm

Abstract

A number of algorithms are available for computing the simulation relation on Kripke structures and on labelled transition systems representing concurrentsystems. Among them, the algorithm by Ranzato and Tapparo~[2007] has the best time complexity, while the algorithm by Gentilini et al.~[2003]~--~successivelycorrected by van Glabbeek and Ploeger~[2008]~--~has thebest space complexity. Both space and time complexities are critical issues in a simulation algorithm, in particular memory requirements are crucial in the context of model checking when dealing with large state spaces.We propose here a new simulation algorithm thatis obtained as a space saving modification of the time efficient algorithm by Ranzato and Tapparo: a symbolic representation of sets is embedded in thisalgorithm so that any set of states manipulated by the algorithm can be efficiently stored as a set of blocks of a suitable state partition. It turns out that this new simulation algorithm retains a space complexity comparable with Gentilini et al.'s algorithm while improving on Gentilini et al.'s time bound.