DRAT Proofs of Unsatisfiability for SAT Modulo Monotonic Theories
Author:
Feng Nick,Hu Alan J.,Bayless Sam,Iqbal Syed M.,Trentin Patrick,Whalen Mike,Pike Lee,Backes John
Abstract
AbstractGenerating proofs of unsatisfiability is a valuable capability of most SAT solvers, and is an active area of research for SMT solvers. This paper introduces the first method to efficiently generate proofs of unsatisfiability specifically for an important subset of SMT: SAT Modulo Monotonic Theories (SMMT), which includes many useful finite-domain theories (e.g., bit vectors and many graph-theoretic properties) and is used in production at Amazon Web Services. Our method uses propositional definitions of the theory predicates, from which it generates compact Horn approximations of the definitions, which lead to efficient DRAT proofs, leveraging the large investment the SAT community has made in DRAT. In experiments on practical SMMT problems, our proof generation overhead is minimal (7.41% geometric mean slowdown, 28.8% worst-case), and we can generate and check proofs for many problems that were previously intractable.
Publisher
Springer Nature Switzerland
Reference39 articles.
1. Armand, M., Faure, G., Grégoire, B., Keller, C., Théry, L., Werner, B.: A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses. In: Jouannaud, J., Shao, Z. (eds.) Certified Programs and Proofs - First International Conference, CPP 2011, Kenting, Taiwan, December 7-9, 2011. Proceedings. Lecture Notes in Computer Science, vol. 7086, pp. 135–150. Springer (2011). https://doi.org/10.1007/978-3-642-25379-9_12, https://doi.org/10.1007/978-3-642-25379-9_12 2. Backes, J., Bayless, S., Cook, B., Dodge, C., Gacek, A., Hu, A.J., Kahsai, T., Kocik, B., Kotelnikov, E., Kukovec, J., McLaughlin, S., Reed, J., Rungta, N., Sizemore, J., Stalzer, M., Srinivasan, P., Subotić, P., Varming, C., Whaley, B.: Reachability analysis for AWS-based networks. In: Dillig, I., Tasiran, S. (eds.) International Conference on Computer Aided Verification (CAV). pp. 231–241. Springer (2019) 3. Baek, S., Carneiro, M., Heule, M.J.H.: 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 — 27th International Conference, TACAS 2021. Lecture Notes in Computer Science, vol. 12651, pp. 59–75. Springer (2021). https://doi.org/10.1007/978-3-030-72016-2_4, https://doi.org/10.1007/978-3-030-72016-2_4 4. Barbosa, H., Blanchette, J., Fleury, M., Fontaine, P., Schurr, H.J.: Better SMT proofs for easier reconstruction. In: AITP 2019-4th Conference on Artificial Intelligence and Theorem Proving (2019) 5. Barbosa, H., Blanchette, J.C., Fontaine, P.: Scalable Fine-Grained Proofs for Formula Processing. In: de Moura, L. (ed.) Automated Deduction - CADE 26 - 26th International Conference on Automated Deduction, Gothenburg, Sweden, August 6-11, 2017, Proceedings. Lecture Notes in Computer Science, vol. 10395, pp. 398–412. Springer (2017). https://doi.org/10.1007/978-3-319-63046-5_25, https://doi.org/10.1007/978-3-319-63046-5_25
|
|