LLM-Assisted Bi-Approximate CHC Solving

Baiting Jiang

Constrained Horn clause (CHC) solvers often struggle to discover deep counterexamples whose derivations may require extensive rule unfolding. Although large language models (LLMs) can propose long-range symbolic relations, prior work on formally checked LLM-assisted verification has mainly focused on generating inductive invariants and concrete traces. We exploit this broader capability through Derivation Power Under-approximations (DPUs). Each DPU is a solver-certified under-approximation of the relation induced by a multi-step CHC derivation. An LLM proposes each DPU with symbolic intermediate-state witnesses that enable SMT validation without introducing additional quantifiers. Validated DPUs can be composed and reused soundly. Building on this mechanism, our LLM-assisted framework HornCraft combines invariant generation for over-approximation with DPU generation for under-approximation in CHC solving. On 260 linear and nonlinear integer-arithmetic CHC-COMP benchmarks left unresolved by a 30-minute Spacer run, HornCraft returns certified verdicts for 228 instances. It certifies 42 instances as unsafe, compared with 22 when DPU construction and reuse are disabled.