Abstract
We introduce FRAT, a new proof format for unsatisfiable SAT problems, and its associated toolchain. Compared to DRAT, the FRAT format allows solvers to include more information in proofs to reduce the computational cost of subsequent elaboration to LRAT. The format is easy to parse forward and backward, and it is extensible to future proof methods. The provision of optional proof steps allows SAT solver developers to balance implementation effort against elaboration time, with little to no overhead on solver time. We benchmark our FRAT toolchain against a comparable DRAT toolchain and confirm >84% median reduction in elaboration time and >94% median decrease in peak memory usage.
Keywords
- Satisfiability
- Proof format
- DRAT
- LRAT
- FRAT
S. Baek and M. Carneiro—Partially supported by AFOSR grant FA9550-18-1-0120
M. J. H. Heule—Supported by the National Science Foundation under grant CCF-2010951
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References
Barbosa, H., Blanchette, J.C., Fleury, M., Fontaine, P.: Scalable fine-grained proofs for formula processing. Journal of Automated Reasoning pp. 1–26 (2019)
Biere, A., Cimatti, A., Clarke, E.M., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361). pp. 317–320. IEEE (1999)
Cruz-Filipe, L., Heule, M.J.H., Hunt, W.A., Kaufmann, M., Schneider-Kamp, P.: Efficient certified RAT verification. In: International Conference on Automated Deduction. pp. 220–236. Springer (2017)
Fleury, M.: Optimizing a verified SAT solver. In: Badger, J.M., Rozier, K.Y. (eds.) NFM. LNCS, vol. 11460, pp. 148–165. Springer (2019)
Fleury, M., Blanchette, J.C., Lammich, P.: A verified SAT solver with watched literals using imperative HOL. In: Andronick, J., Felty, A.P. (eds.) CPP. pp. 158–171. ACM (2018)
Goldberg, E., Novikov, Y.: Verification of proofs of unsatisfiability for CNF formulas. In: Proceedings of the conference on Design, Automation and Test in Europe-Volume 1. p. 10886. IEEE Computer Society (2003)
Haken, A.: The intractability of resolution. Theoretical Computer Science 39, 297–308 (1985)
Heule, M.J.H.: The DRAT format and DRAT-trim checker. arXiv preprint \({\rm {arXiv}}\):1610.06229 (2016)
Heule, M.J.H., Biere, A.: Clausal proof compression. In: International Workshop on the Implementation of Logics (2015)
Heule, M.J.H., Hunt, W.A., Wetzler, N.: Verifying refutations with extended resolution. In: International Conference on Automated Deduction. pp. 345–359. Springer (2013)
Heule, M.J.H., Hunt, W.A., Wetzler, N.: Bridging the gap between easy generation and efficient verification of unsatisfiability proofs. Softw. Test. Verif. Reliab. 24(8), 593–607 (Sep 2014)
Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing. pp. 228–245. Springer (2016)
Järvisalo, M., Heule, M.J.H., Biere, A.: Inprocessing rules. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR. LNCS, vol. 7364, pp. 355–370. Springer (2012)
Kautz, H., Selman, B.: Pushing the envelope: Planning, propositional logic, and stochastic search. In: Proceedings of the National Conference on Artificial Intelligence. pp. 1194–1201 (1996)
Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional (2015)
Lammich, P.: The GRAT tool chain. In: International Conference on Theory and Applications of Satisfiability Testing. pp. 457–463. Springer (2017)
Lammich, P.: Efficient verified (un) SAT certificate checking. Journal of Automated Reasoning pp. 1–20 (2019)
Marić, F.: Formal verification of a modern SAT solver by shallow embedding into Isabelle/HOL. Theoretical Computer Science 411(50), 4333–4356 (2010)
Oe, D., Stump, A., Oliver, C., Clancy, K.: versat: A verified modern SAT solver. In: International Workshop on Verification, Model Checking, and Abstract Interpretation. pp. 363–378. Springer (2012)
Shankar, N., Vaucher, M.: The mechanical verification of a dpll-based satisfiability solver. Electronic Notes in Theoretical Computer Science 269, 3 – 17 (2011), proceedings of the Fifth Logical and Semantic Frameworks, with Applications Workshop (LSFA 2010)
Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) Theory and Applications of Satisfiability Testing - SAT 2009, 12th International Conference, SAT 2009, Swansea, UK, June 30 - July 3, 2009. Proceedings. Lecture Notes in Computer Science, vol. 5584, pp. 244–257. Springer (2009)
Sörensson, N., Biere, A.: Minimizing learned clauses. In: Kullmann, O. (ed.) Theory and Applications of Satisfiability Testing - SAT 2009. pp. 237–243. Springer Berlin Heidelberg, Berlin, Heidelberg (2009)
Stump, A., Oe, D., Reynolds, A., Hadarean, L., Tinelli, C.: SMT proof checking using a logical framework. Formal Methods in System Design 42(1), 91–118 (2013)
Sutcliffe, G., Zimmer, J., Schulz, S.: Tstp data-exchange formats for automated theorem proving tools. Distributed Constraint Problem Solving and Reasoning in Multi-Agent Systems 112, 201–215 (2004)
Van Gelder, A.: Improved conflict-clause minimization leads to improved propositional proof traces. In: Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing. p. 141–146. SAT ’09, Springer-Verlag, Berlin, Heidelberg (2009)
Wetzler, N., Heule, M.J.H., Hunt, W.A.: Mechanical verification of SAT refutations with extended resolution. In: International Conference on Interactive Theorem Proving. pp. 229–244. Springer (2013)
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Baek, S., Carneiro, M., Heule, M.J.H. (2021). A Flexible Proof Format for SAT Solver-Elaborator Communication. In: Groote, J.F., Larsen, K.G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2021. Lecture Notes in Computer Science(), vol 12651. Springer, Cham. https://doi.org/10.1007/978-3-030-72016-2_4
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