Can LLMs Reason Like Automated Theorem Provers for Rust Verification? VCoT-Bench: Evaluating via Verification Chain of Thought

Large Language Models (LLMs) have shown promising results in automating formal verification. However, existing approaches treat proof generation as a static, end-to-end prediction over source code, relying on limited verifier feedback and lacking access to concrete program behaviors. We present EXVERUS, a counterexample-guided framework that enables LLMs to reason about proofs using behavioral feedback via counterexamples. When a proof fails, EXVERUS automatically generates and validates counterexamples, and then guides the LLM to generalize them into inductive invariants to block these failures. Our evaluation shows that EXVERUS significantly improves proof accuracy, robustness, and token efficiency over the state-of-the-art prompting-based Verus proof generator.

Verification is becoming central to both reinforcement-learning-based training and inference-time control of large language models (LLMs). Yet current verifiers face a fundamental trade-off: LLM-based verifiers are expressive but hard to control and prone to error, while deterministic executable verifiers are reliable and interpretable but often limited in capability. We study the following question: given a development set of LLM outputs and labels for a target objective, such as correctness, can we automatically induce a minimal set of Python verifiers whose joint satisfaction closely matches that objective? We propose AutoPyVerifier, a framework that uses an LLM to synthesize candidate verifier functions and then refines them through search over a directed acyclic graph (DAG). By navigating the DAG, AutoPyVerifier systematically explores the space of deterministic executable verifiers and selects a compact verifier set whose joint satisfaction best approximates the target objective. Across mathematical reasoning, coding, function calling, and instruction-following benchmarks for several state-of-the-art LLMs, AutoPyVerifier improves target-objective prediction by up to 55.0 F1 points over the initial LLM-generated verifier sets. Additional analyses show that the most useful verification targets vary by benchmark and model, and that the DAG-based search shifts the learned verifier sets toward more structural and semantically grounded checks. We further show that exposing the discovered verifier set to an LLM as an external tool improves downstream accuracy by up to 17.0 points. We release our code

Scaling pre-training, post-training, and test-time compute have become the central paradigms for improving the capabilities of LLMs. In this work, we identify verification, the ability to determine the correctness of a solution, as a new scaling axis. To unlock this and demonstrate its effectiveness, we introduce LLM-as-a-Verifier, a general-purpose verification framework that provides fine-grained feedback for agentic tasks without requiring additional training. Unlike standard LM judges that prompt LLMs to produce discrete scores for candidate solutions, LLM-as-a-Verifier computes the expectation over the distribution of scoring token logits to generate continuous scores. This probabilistic formulation enables verification to scale along multiple dimensions: (1) score granularity, (2) repeated evaluation, and (3) criteria decomposition. In particular, we show that scaling the scoring granularity leads to better separation between positive and negative solutions, resulting in more calibrated comparisons. Moreover, scaling repeated evaluation and criteria decomposition consistently lead to additional gains in verification accuracy through variance and complexity reduction. We further introduce a cost-efficient ranking algorithm for selecting the best solution among candidates using the verifier's continuous scores. LLM-as-a-Verifier achieves state-of-the-art performance on Terminal-Bench V2 (86.5%), SWE-Bench Verified (78.2%), RoboRewardBench (87.4%), and MedAgentBench (73.3%). Beyond verification, the fine-grained signals from LLM-as-a-Verifier can also serve as a proxy for estimating task progress. We build an extension for Claude Code, enabling developers to monitor and improve their own agentic systems. Finally, we show that LLM-as-a-Verifier can provide dense feedback for RL, improving the sample efficiency of SAC and GRPO on robotics and mathematical reasoning benchmarks.