Amino acid sequence of the small core protein from bacteriophage φX174

Refinement checking plays an important role in system verification. This means that the correctness of the system is established by showing a refinement relation between two models; one for the implementation and one for the specification. Wang \{et al. describe an algorithm based on antichains for efficiently deciding stable failures refinement and failures-divergences refinement. We identify several issues pertaining to the correctness and performance in these algorithms and propose new, correct, antichain-based algorithms. Using a number of experiments we show that our algorithms outperform the original ones in terms of running time and memory usage.