An efficient simulation algorithm based on abstract interpretation

A number of algorithms for computing the simulation preorder are available. Let Σ denote the state space, ! the transition relation and Psim 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. 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(|Psim||!|)-time while the space complexity is in O(|Psim| + |Σ| log |Psim|). 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(|Psim||!|)-time and O(|Psim||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. An experimental evaluation showed good comparative results with respect to Henzinger, Henzinger and Kopke’s algorithm.