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ORSMT: Unleashing the Potential of Satisfiability Modulo Theories for Semantic Verification and Repair in LLM-Based Optimization

Rui Zhang, Chenyu Zhou, Jianghao Lin, Yaoxin Wu, Dongdong Ge, 宋文 · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29145 · cited by 0 works (OpenAlex) · open-access PDF

Korean

대형 언어 모델은 자연 언어 문제에서 최적화 모델링을 점점 더 자동화하여 글쓰기 수학, 솔버 코드 및 반환 보고서를 생성합니다. 이러한 유물들에 걸쳐 하나의 최적화 문제를 검증하는 것은 정의 비교를 필요로합니다 : 불평등한 모델은 동일한 목표를 달성 할 수 있으며, 동등한 모델은 다른 보조 변수를 사용할 수 있으며, 상호 일관된 유물은 동일한 소스 요건을 제거 할 수 있습니다. ORSMT는 다른 유형의 정의 문자 인터페이스와 정확한 SMT 관계 쿼리를 제공합니다. 관찰 가능한 결정, 프로젝트 보조 변수, 실현 가능한 영역 및 객관적 관계를 증명하거나 반박하고, 암시된 행 또는 도메인 및 링크 소스 텍스트에 대한 거부

Machine translation (Meta M2M100); the English original follows.

Abstract

Large language models increasingly automate optimization modeling from natural language problems, producing written mathematics, solver code and a returned report. Verifying one optimization problem across these artifacts requires semantic comparison: unequal models can attain the same objective, equivalent models can use different auxiliary variables, and mutually consistent artifacts can omit the same source requirement. ORSMT provides a typed semantic interface and exact SMT relation queries. It aligns observable decisions, projects auxiliary variables, proves or refutes feasible region and objective relations, localizes refutations to implicated rows or domains and links source texts when available. It then reconstructs one artifact from another, and each adopted candidate passes the required relation checks. Across 3,034 problems and six generator sizes, ORSMT improves the model-code match rate in all 72 benchmark and generator combinations before selection. Protected selection raises the aggregate rate from 43.2% to 88.2% and the share that are both correct and matched from 25.2% to 40.2%. On the 1,905 refuted outputs, certified voting under the shared fallback makes 50.9% of outputs correct and matched, compared with 44.8% for ReLoop and 49.4% for Opt-Verifier. A separate one-round source revision followed by exact reconstruction restores a model-code match for 84.4% of the refuted pairs.

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Topics: Computer science, Artifact (error), Generator (circuit theory), Satisfiability modulo theories, Solver, Theoretical computer science

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