{"corr_author":"1","external_id":{"arxiv":["2412.16226"]},"date_created":"2025-05-11T22:02:39Z","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020"}],"scopus_import":"1","title":"Quantified linear and polynomial arithmetic satisfiability via template-based skolemization","publication_status":"published","publication":"Proceedings of the AAAI Conference on Artificial Intelligence","day":"11","ec_funded":1,"_id":"19667","department":[{"_id":"KrCh"}],"author":[{"orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"full_name":"Kafshdar Goharshadi, Ehsan","first_name":"Ehsan","last_name":"Kafshdar Goharshadi","id":"103b4fa0-896a-11ed-bdf8-87b697bef40d","orcid":"0000-0002-8595-0587"},{"id":"67638922-f394-11eb-9cf6-f20423e08757","last_name":"Karrabi","first_name":"Mehrdad","full_name":"Karrabi, Mehrdad"},{"first_name":"Harshit J.","last_name":"Motwani","full_name":"Motwani, Harshit J."},{"first_name":"Maximilian","last_name":"Seeliger","full_name":"Seeliger, Maximilian"},{"full_name":"Zikelic, Dorde","orcid":"0000-0002-4681-1699","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic","first_name":"Dorde"}],"issue":"11","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2374-3468"],"issn":["2159-5399"]},"type":"conference","abstract":[{"text":"The problem of checking satisfiability of linear real arithmetic (LRA) and non-linear real arithmetic (NRA) formulas has broad applications, in particular, they are at the heart of logic-related applications such as logic for artificial intelligence, program analysis, etc. While there has been much work on checking satisfiability of unquantified LRA and NRA formulas, the problem of checking satisfiability of quantified LRA and NRA formulas remains a significant challenge. The main bottleneck in the existing methods is a computationally expensive quantifier elimination step. In this work, we propose a novel method for efficient quantifier elimination in quantified LRA and NRA formulas. We propose a template-based Skolemization approach, where we automatically synthesize linear/polynomial Skolem functions in order to eliminate quantifiers in the formula. The key technical ingredient in our approach are Positivstellensätze theorems from algebraic geometry, which allow for an efficient manipulation of polynomial inequalities. Our method offers a range of appealing theoretical properties combined with a strong practical performance. On the theory side, our method is sound, semi-complete, and runs in subexponential time and polynomial space, as opposed to existing sound and complete quantifier elimination methods that run in doubly-exponential time and at least exponential space. On the practical side, our experiments show superior performance compared to state of the art SMT solvers in terms of the number of solved instances and runtime, both on LRA and on NRA benchmarks.","lang":"eng"}],"year":"2025","month":"04","article_processing_charge":"No","status":"public","oa":1,"date_updated":"2025-05-12T08:52:47Z","OA_type":"green","volume":39,"citation":{"ista":"Chatterjee K, Goharshady E, Karrabi M, Motwani HJ, Seeliger M, Zikelic D. 2025. Quantified linear and polynomial arithmetic satisfiability via template-based skolemization. Proceedings of the AAAI Conference on Artificial Intelligence. AAAI: Conference on Artificial Intelligence vol. 39, 11158–11166.","apa":"Chatterjee, K., Goharshady, E., Karrabi, M., Motwani, H. J., Seeliger, M., &#38; Zikelic, D. (2025). Quantified linear and polynomial arithmetic satisfiability via template-based skolemization. In <i>Proceedings of the AAAI Conference on Artificial Intelligence</i> (Vol. 39, pp. 11158–11166). Philadelphia, PA, United States: Association for the Advancement of Artificial Intelligence. <a href=\"https://doi.org/10.1609/aaai.v39i11.33213\">https://doi.org/10.1609/aaai.v39i11.33213</a>","ieee":"K. Chatterjee, E. Goharshady, M. Karrabi, H. J. Motwani, M. Seeliger, and D. Zikelic, “Quantified linear and polynomial arithmetic satisfiability via template-based skolemization,” in <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, Philadelphia, PA, United States, 2025, vol. 39, no. 11, pp. 11158–11166.","chicago":"Chatterjee, Krishnendu, Ehsan Goharshady, Mehrdad Karrabi, Harshit J. Motwani, Maximilian Seeliger, and Dorde Zikelic. “Quantified Linear and Polynomial Arithmetic Satisfiability via Template-Based Skolemization.” In <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, 39:11158–66. Association for the Advancement of Artificial Intelligence, 2025. <a href=\"https://doi.org/10.1609/aaai.v39i11.33213\">https://doi.org/10.1609/aaai.v39i11.33213</a>.","short":"K. Chatterjee, E. Goharshady, M. Karrabi, H.J. Motwani, M. Seeliger, D. Zikelic, in:, Proceedings of the AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence, 2025, pp. 11158–11166.","ama":"Chatterjee K, Goharshady E, Karrabi M, Motwani HJ, Seeliger M, Zikelic D. Quantified linear and polynomial arithmetic satisfiability via template-based skolemization. In: <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>. Vol 39. Association for the Advancement of Artificial Intelligence; 2025:11158-11166. doi:<a href=\"https://doi.org/10.1609/aaai.v39i11.33213\">10.1609/aaai.v39i11.33213</a>","mla":"Chatterjee, Krishnendu, et al. “Quantified Linear and Polynomial Arithmetic Satisfiability via Template-Based Skolemization.” <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, vol. 39, no. 11, Association for the Advancement of Artificial Intelligence, 2025, pp. 11158–66, doi:<a href=\"https://doi.org/10.1609/aaai.v39i11.33213\">10.1609/aaai.v39i11.33213</a>."},"date_published":"2025-04-11T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Association for the Advancement of Artificial Intelligence","intvolume":"        39","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2412.16226","open_access":"1"}],"OA_place":"repository","arxiv":1,"oa_version":"Preprint","acknowledgement":"This work was partially funded by ERC CoG 863818 (ForM-SMArt) and Austrian Science Fund (FWF) 10.55776/COE12.","doi":"10.1609/aaai.v39i11.33213","page":"11158-11166","conference":{"location":"Philadelphia, PA, United States","start_date":"2025-02-25","end_date":"2025-03-04","name":"AAAI: Conference on Artificial Intelligence"},"quality_controlled":"1"}