{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/automated-proof-of-polynomial-inequalities","title":"Automated Proof of Polynomial Inequalities via Reinforcement Learning","arxiv_id":"2503.06592","date":"2025-03-09","proceeding":"CVPR 2025 1","authors":["Banglong Liu","Niuniu Qi","Xia Zeng","Lydia Dehbi","Zhengfeng Yang"],"abstract":"Polynomial inequality proving is fundamental to many mathematical disciplines and finds wide applications in diverse fields. Current traditional algebraic methods are based on searching for a polynomial positive definite representation over a set of basis. However, these methods are limited by truncation degree. To address this issue, this paper proposes an approach based on reinforcement learning to find a {Krivine-basis} representation for proving polynomial inequalities. Specifically, we formulate the inequality proving problem as a linear programming (LP) problem and encode it as a basis selection problem using reinforcement learning (RL), achieving a non-negative {Krivine basis}. Moreover, a fast multivariate polynomial multiplication method based on Fast Fourier Transform (FFT) is employed to enhance the efficiency of action space search. Furthermore, we have implemented a tool called {APPIRL} (Automated Proof of Polynomial Inequalities via Reinforcement Learning). Experimental evaluation on benchmark problems demonstrates the feasibility and effectiveness of our approach. In addition, {APPIRL} has been successfully applied to solve the maximum stable set problem.","url_abs":"https://arxiv.org/abs/2503.06592v1","url_pdf":"https://arxiv.org/pdf/2503.06592v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"automated-proof-of-polynomial-inequalities","repo_url":"https://github.com/blliu6/appirl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2503.06592","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2503.06592"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"deterministic:regex_extraction","url":"https://github.com/blliu6/APPIRL","reach":null}],"summary":{"ran":1,"unverified":2},"by_repo_kind":{"official":{"samples":3,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":3,"samples":[{"code_sha256_prefix":"952f4a31e0cb4ab3","entry":"Qnet","repo":"blliu6/APPIRL","repo_kind":"official","path":"proof/dqn.py","file_url":"https://github.com/blliu6/APPIRL/blob/HEAD/proof/dqn.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"952f4a31e0cb4ab3"}},{"code_sha256_prefix":"481aca1daf0d80ec","entry":"DQN","repo":"blliu6/APPIRL","repo_kind":"official","path":"proof/dqn.py","file_url":"https://github.com/blliu6/APPIRL/blob/HEAD/proof/dqn.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"481aca1daf0d80ec"}},{"code_sha256_prefix":"6f0163b896fab854","entry":"ProofConfig","repo":"blliu6/APPIRL","repo_kind":"official","path":"proof/dqn.py","file_url":"https://github.com/blliu6/APPIRL/blob/HEAD/proof/dqn.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"6f0163b896fab854"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}