Aditya Vempaty, Himaneesh Sompalle, Manan Tayal, Mowafak Allaham, Prasenjit Dey, Ashish Jagmohan, Ravi Kokku
What should ``verified'' mean when evaluating LLM-generated code? Many existing pipelines report a single verification number. We argue this collapses three distinct properties measured in a conditional audit sequence: verifier acceptance (Surface A), \emph{syntactic specification binding (Surface B: does the proof obligation bind to the spec?), and \emph{semantic specification fidelity} (Surface C: does the spec capture the informal requirement?). Two empirical demonstrations show the surfaces separate. \textbf{First ($A \neq B$), via Li@Opus (a same-model reproduction of \citet{li2025dafny}'s Dafny-as-intermediate-representation (IR) pipeline under Claude Opus 4.7) on three Python benchmarks}: it reaches \textbf{99.1\% verifier acceptance} on HumanEval while only \textbf{1.9\%} carry a certificate binding to a spec-defined predicate or function. \textbf{Second ($B \neq C$), via VCG on two Rust benchmarks}: we use VCG (which is our own in-house Dafny-as-intermediate pipeline) on Rust because the Rust target lets us enforce fully-verifiable output (every component ships as a Dafny certificate, ensures-binding gate passing by construction). Even inside that construction, \textbf{11.48\% (MBPP-Rust) and 14.82\% (VeriContest LC slice) of structurally-verified samples still fail hidden tests}. On the LC slice of VeriContest, \textbf{VCG's reported End2End rate is 7.79\% (535/6870).} The cited external rates are 5.51\% (GPT-5.5) and 1.88\% (single-shot Opus 4.7). These give descriptive differences of 2.3 percentage points and 4.14$\times$, respectively; task-budget, repair and harness differences prevent a matched-performance claim.
Offline reinforcement learning (RL) offers a promising framework for deploying autonomous systems in safety-critical settings without the risks of online exploration. However, learning policies that simultaneously achieve high performance and strong safety guarantees from fixed datasets remains a fundamental challenge. Many existing safe offline RL approaches typically rely on soft constraint formulations, which may permit safety violations and are sensitive to distributional shift. In contrast, formal methods such as Hamilton--Jacobi (HJ) reachability and Control Barrier Functions (CBFs) provide rigorous safety guarantees, but often yield overly conservative solutions, often neglecting performance. In this work, we bridge this gap by formulating safe offline RL as a state-constrained optimal control problem, where safety is enforced through hard state constraints and performance is captured via a reward function. The resulting value function satisfies a Hamilton--Jacobi--Bellman (HJB) equation, which we approximate using offline RL on fixed datasets by learning an epigraph feasibility value function and extracting policies via flow matching. This formulation enables principled integration of safety guarantees with data-driven policy optimization. Empirically, across safety-critical benchmarks including boat navigation, Safety-Gymnasium, and Bullet-Safety-Gym tasks, our approach achieves competitive returns while exhibiting near-zero constraint violations, demonstrating a favorable balance between safety and performance in the offline setting.