Dimension-parametric verification of optimization formulations

Extend SOVER’s SMT-based reformulation verifier beyond bounded, fixed-dimension instances to dimension-parametric formulations, thereby providing stronger guarantees for entire families of optimization problems.

Background

SOVER currently verifies instantiated optimization formulations after bounded unrolling of indexed variables and matrix expressions to a fixed proxy dimension. The paper notes that verifying formulations parametrically in their dimension would require additional induction or quantified-array reasoning. The authors explicitly identify this extension as an open direction because it would strengthen certification from individual instances to problem families.

References

Several directions remain open. Improving LLM-based mapping synthesis could reduce inconclusive cases, while extending the verifier beyond bounded instances to dimension-parametric formulations would provide stronger guarantees for problem families.

— SOVER: Formal Certification of Optimization Reformulations via LLM-Assisted SMT Verification  (2609.00728 - Bhattacharyya et al., 1 Sep 2026) in Section 5, Conclusion and Future Work