An efficient simulation algorithm based on abstract interpretation

Abstract

A number of algorithms for computing the simulation preorder and equivalence are available. Let Σ denote the state space, → the transition relation and P sim the partition of Σ induced by simulation equivalence. The algorithms by Henzinger, Henzinger, Kopke and by Bloom and Paige run in O ( | Σ | | → | ) -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 Σ . 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 sim | 2 | → | ) -time while the space complexity is in O ( | P sim | 2 + | Σ | log | P sim | ) . 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 sim | | → | ) -time and O ( | P sim | | Σ | log | Σ | ) -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 | Σ | . An experimental evaluation showed good comparative results with respect to Henzinger, Henzinger and Kopke’s algorithm.