AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-23
LLM2Cert: LLM Synthesis of Certificates with SMT/Lean Verification
Lyapunov functions and barrier certificates guarantee stability and safety for dynamical systems, but synthesizing and verifying them remains difficult for nonlinear, high-dimensional systems. The authors introduce DynaCertBench, a benchmark of 105 instances, and LLM2Cert, an LLM-driven framework that synthesizes candidate certificates and routes each proof obligation to an SMT solver or the Lean Proof-Repair agent. LLM2Cert verifies 81 of the 105 instances (77.1%), 17.1 percentage points more than one-shot proposal without feedback, and verifies 22 certificates that All-SMT leaves unresolved.