Correcting a Space-Efficient Simulation Algorithm

TLDR: In this paper, the authors show that the fixed-point theory is flawed and correct the algorithm without affecting its space and time complexity, and they show how the fixed point operator can be repaired, and that the algorithm is incorrect.

Abstract: Although there are many efficient algorithms for calculating the simulation preorder on finite Kripke structures, only two have been proposed of which the space complexity is of the same order as the size of the output of the algorithm. Of these, the one with the best time complexity exploits the representation of the simulation problem as a generalised coarsest partition problem. It is based on a fixed-point operator for obtaining a generalised coarsest partition as the limit of a sequence of partition pairs. We show that this fixed-point theory is flawed, and that the algorithm is incorrect. Although we do not see how the fixed-point operator can be repaired, we correct the algorithm without affecting its space and time complexity.