Abstract
Mutilated chessboard problems have been called a “tough nut to crack” for automated reasoning. They are, for instance, hard for resolution, resulting in exponential runtime of current SAT solvers. Although there exists a well-known short argument for solving mutilated chessboard problems, this argument is based on an abstraction that is challenging to discover by automated-reasoning techniques. In this paper, we present another short argument that is much easier to compute and that can be expressed within the recent (clausal) \(\mathsf {PR}\) proof system for propositional logic. We construct short clausal proofs of mutilated chessboard problems using this new argument and validate them using a formally-verified proof checker.
Supported by NSF under grant CCF-1813993, by AFRL Award FA8750-15-2-0096, Austrian Science Fund (FWF) under projects W1255-N23 and S11409-N23 (RiSE) and the LIT Secure and Correct Systems Lab funded by the State of Upper Austria.
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Acknowledgements
The authors thank Alexey Porkhunov for contributing the mutilated chessboard formulas to the 2018 SAT Competition and for his suggestion to study these formulas in the context of the \(\mathsf {PR}\) proof system, and also thank Jasmin Blanchette for his comments on an earlier version of this paper.
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Heule, M.J.H., Kiesl, B., Biere, A. (2019). Clausal Proofs of Mutilated Chessboards. In: Badger, J., Rozier, K. (eds) NASA Formal Methods. NFM 2019. Lecture Notes in Computer Science(), vol 11460. Springer, Cham. https://doi.org/10.1007/978-3-030-20652-9_13
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DOI: https://doi.org/10.1007/978-3-030-20652-9_13
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