An efficient simulation algorithm based on abstract interpretation

• Authors: Francesco Ranzato;Francesco Tapparo
• Venue: Information and Computation
• Year: 2010

A number of algorithms for computing the simulation preorder and equivalence are available. Let @S denote the state space, - the transition relation and P"s"i"m the partition of @S induced by simulation equivalence. The algorithms by Henzinger, Henzinger, Kopke and by Bloom and Paige run in O(|@S||-|)-time and, as far as time complexity is concerned, they are the best available algorithms. However, these algorithms have the drawback of a space complexity that is more than quadratic in the size of the state space @S. The algorithm by Gentilini, Piazza, Policriti - subsequently corrected by van Glabbeek and Ploeger - appears to provide the best compromise between time and space complexity. Gentilini et al.'s algorithm runs in O(|P"s"i"m|^2|-|)-time while the space complexity is in O(|P"s"i"m|^2+|@S|log|P"s"i"m|). We present here a new efficient simulation algorithm that is obtained as a modification of Henzinger et al.'s algorithm and whose correctness is based on some techniques used in applications of abstract interpretation to model checking. Our algorithm runs in O(|P"s"i"m||-|)-time and O(|P"s"i"m||@S|log|@S|)-space. Thus, this algorithm improves the best known time bound while retaining an acceptable space complexity that is in general less than quadratic in the size of the state space |@S|. An experimental evaluation showed good comparative results with respect to Henzinger, Henzinger and Kopke's algorithm.