Saving space in a time efficient simulation algorithm

A number of algorithms for computing the simulation preorder on Kripke structures and on labelled transition systems are available. Among them, the algorithm by Ranzato and Tapparo [2007] has the best time complexity,while the algorithm by Gentilini et al. [2003] – successively corrected by van Glabbeek and Ploeger [2008] – has the best 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. Here, we propose a new simulation algorithm that is obtained as a space saving modification of the time efficient algorithm by Ranzato and Tapparo: a symbolic representation of sets is embedded in this algorithm 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 novel simulation algorithm has a space complexity comparable with Gentilini et al.'s algorithm while improving on Gentilini et al.'s time bound.