A Parity Game Tale of Two Counters

07/26/2018

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by   Tom van Dijk, et al.

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Parity games have important practical applications in formal verification and synthesis, especially for problems related to linear temporal logic and to the modal mu-calculus. The problem is believed to admit a solution in polynomial time, motivating researchers to find candidates for such an algorithm and to defeat these algorithms. We present a parameterized parity game called the Two Counters game, which provides an exponential lower bound for a wide range of parity game solving algorithms. We are the first to provide an exponential lower bound to priority promotion with the delayed promotion policy, and the first to provide such a lower bound to tangle learning.