Refinement checking plays an important role in system verification. It establishes properties of an implementation by showing a refinement relationship between the implementation and a specification. Recently, it has been shown that anti-chain based approaches increase the efficiency of trace refinement checking significantly. In this work, we study the problem of adopting anti-chain for stable failures refinement checking, failures-divergence refinement checking and probabilistic refine

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... g (i.e., a probabilistic implementation against a nonprobabilistic specification). We show that the first two problems can be significantly improved, because the state space of the product model may be reduced dramatically. Though applying anti-chain for probabilistic refinement checking is more complicated, we manage to show improvements in some cases. We have integrated these techniques into the PAT model checking framework. Experiments are conducted to demonstrate the efficiency of our approach.