Formally Certified Approximate Model Counting
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| Název: | Formally Certified Approximate Model Counting |
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| Autoři: | Tan, Yong Kiam, Yang, Jiong, Soos, Mate, Myreen, Magnus, 1983, Meel, Kuldeep S. |
| Zdroj: | De nästa 700 verifierade kompilatorerna 36th International Conference on Computer Aided Verification, CAV 2024, Montreal, Canada Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 14681 LNCS:153-177 |
| Témata: | randomized algorithms, formal verification, proof certification, approximate model counting |
| Popis: | Approximate model counting is the task of approximating the number of solutions to an input Boolean formula. The state-of-the-art approximate model counter for formulas in conjunctive normal form (CNF), ApproxMC, provides a scalable means of obtaining model counts with probably approximately correct (PAC)-style guarantees. Nevertheless, the validity of ApproxMC’s approximation relies on a careful theoretical analysis of its randomized algorithm and the correctness of its highly optimized implementation, especially the latter’s stateful interactions with an incremental CNF satisfiability solver capable of natively handling parity (XOR) constraints. We present the first certification framework for approximate model counting with formally verified guarantees on the quality of its output approximation. Our approach combines: (i) a static, once-off, formal proof of the algorithm’s PAC guarantee in the Isabelle/HOL proof assistant; and (ii) dynamic, per-run, verification of ApproxMC’s calls to an external CNF-XOR solver using proof certificates. We detail our general approach to establish a rigorous connection between these two parts of the verification, including our blueprint for turning the formalized, randomized algorithm into a verified proof checker, and our design of proof certificates for both ApproxMC and its internal CNF-XOR solving steps. Experimentally, we show that certificate generation adds little overhead to an approximate counter implementation, and that our certificate checker is able to fully certify 84.7% of instances with generated certificates when given the same time and memory limits as the counter. |
| Popis souboru: | electronic |
| Přístupová URL adresa: | https://research.chalmers.se/publication/542381 https://research.chalmers.se/publication/542381/file/542381_Fulltext.pdf |
| Databáze: | SwePub |
Nájsť tento článok vo Web of Science | Abstrakt: | Approximate model counting is the task of approximating the number of solutions to an input Boolean formula. The state-of-the-art approximate model counter for formulas in conjunctive normal form (CNF), ApproxMC, provides a scalable means of obtaining model counts with probably approximately correct (PAC)-style guarantees. Nevertheless, the validity of ApproxMC’s approximation relies on a careful theoretical analysis of its randomized algorithm and the correctness of its highly optimized implementation, especially the latter’s stateful interactions with an incremental CNF satisfiability solver capable of natively handling parity (XOR) constraints. We present the first certification framework for approximate model counting with formally verified guarantees on the quality of its output approximation. Our approach combines: (i) a static, once-off, formal proof of the algorithm’s PAC guarantee in the Isabelle/HOL proof assistant; and (ii) dynamic, per-run, verification of ApproxMC’s calls to an external CNF-XOR solver using proof certificates. We detail our general approach to establish a rigorous connection between these two parts of the verification, including our blueprint for turning the formalized, randomized algorithm into a verified proof checker, and our design of proof certificates for both ApproxMC and its internal CNF-XOR solving steps. Experimentally, we show that certificate generation adds little overhead to an approximate counter implementation, and that our certificate checker is able to fully certify 84.7% of instances with generated certificates when given the same time and memory limits as the counter. |
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| ISSN: | 16113349 03029743 |
| DOI: | 10.1007/978-3-031-65627-9_8 |