Abstract
We prove that extended resolution—a well-known proof system introduced by Tseitin—polynomially simulates \({\mathsf {DRAT}}\), the standard proof system in modern SAT solving. Our simulation procedure takes as input a \({\mathsf {DRAT}}\) proof and transforms it into an extended-resolution proof whose size is only polynomial with respect to the original proof. Based on our simulation, we implemented a tool that transforms \({\mathsf {DRAT}}\) proofs into extended-resolution proofs. We ran our tool on several benchmark formulas to estimate the increase in size caused by our simulation in practice. Finally, as a side note, we show how blocked-clause addition—a generalization of the extension rule from extended resolution—can be used to replace the addition of resolution asymmetric tautologies in \({\mathsf {DRAT}}\) without introducing new variables.
This work has been supported by the National Science Foundation under grant CCF-1618574, by the Austrian Science Fund (FWF) under project W1255-N23, and by Microsoft Research through its PhD Scholarship Programme.
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Notes
- 1.
The simulation tool, checkers, formulas, and proofs discussed in this section are available on http://www.cs.utexas.edu/~marijn/drat2er.
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Kiesl, B., Rebola-Pardo, A., Heule, M.J.H. (2018). Extended Resolution Simulates DRAT. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds) Automated Reasoning. IJCAR 2018. Lecture Notes in Computer Science(), vol 10900. Springer, Cham. https://doi.org/10.1007/978-3-319-94205-6_34
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