Graph Construction and Matching for Imperative Programs using Neural and Structural Methods

Verified code generation asks a large language model (LLM) to generate both an executable program and a machine-checkable proof that the program meets a formal specification, promising software that is correct by construction. The de facto workflow decouples the two halves of the problem: first synthesize a program, then attempt to prove it correct. We observe that this sequential pipeline can be both ineffective and inefficient in practice. A program generated without anticipating its proof can be subtly incorrect or structurally difficult to verify, forcing the LLM into brittle repair loops that alternate between patching the code and patching the proof. Inspired by Dijkstra's view that a program and its correctness argument should be developed hand in hand, we propose $P^3$, an LLM-based agentic workflow that first derives a unified program-and-proof plan from the specification, then elaborates the implementation and proof scaffold under this shared plan. To evaluate verified code generation in realistic settings, we further introduce Lean4Commit0, a repository-derived, library-level benchmark built by extracting core APIs from real-world software repositories and translating their requirements, including relational specifications across APIs, into Lean tasks. Using four frontier LLM backends, we evaluate $P^3$ on Verina, AlgoVeri, and our Lean4Commit0 benchmark, where it achieves the highest solve rate in every benchmark--model setting. Compared with the stronger baseline, it improves solve rates by 4.6--11.2 percentage points and reduces per-task API cost by up to roughly 40% and wall-clock time by up to roughly 37% on the difficult subset of each benchmark. A targeted ablation further shows gains of 3.3--8.3 points over implementation-only planning, isolating the benefit of planning the program and proof jointly.

Recent advances in Large Language Models (LLMs) have enabled workflows that generate SystemVerilog Assertions (SVAs) from natural-language specifications, with the potential to accelerate Formal Verification (FV). However, high-quality assertion synthesis remains challenging because specifications are often ambiguous or incomplete and critical micro-architectural details reside in the Register Transfer Level (RTL). Many existing approaches treat the specification and RTL as loosely structured text, which weakens specification-to-RTL grounding and leads to semantic mismatches and frequent syntax failures during formal parsing and elaboration. This work addresses these limitations with a verification-centric Knowledge Graph (KG) constructed from structured Intermediate Representations (IRs) extracted from the specification, RTL, and formal-tool feedback, including syntax diagnostics, Counterexamples (CEXs), and coverage reports. The KG links requirements, design hierarchy, signals, assumptions, and properties to provide traceable, design-grounded context for generation. A multi-agent workflow queries and updates this KG to generate SVAs and to drive three refinement loops: syntax repair guided by tool diagnostics, CEX-guided correction using trace links, and coverage-directed property augmentation. Evaluation across seven benchmark designs indicates that KG-based context retrieval improves specification-to-RTL grounding and consistently produces compilable SVAs with low syntax-repair overhead. The approach achieves formal coverage ranging from 78.5% to 99.4%, though convergence exhibits design dependence with complex temporal and arithmetic reasoning remaining challenging for current LLM capabilities.

Program verification is crucial for software correctness, but producing fully verified programs remains difficult in practice. This paper studies whether implementation structure affects automated verifiability when multiple generated programs are intended to satisfy the same task-level semantics. We present Diversify2Verify, a staged LLM-based pipeline for Why3 that infers representation-specific contracts, generates and tests diverse recursive and imperative array/list implementations, and attempts verification with bounded verifier-guided annotation repair. We also construct a verification-oriented benchmark of 73 tasks over integers, arrays, and lists, yielding 292 implementation variants. Diversify2Verify verifies 96 artifacts initially and 154 after two repair passes, improving artifact-level verification from 32.9% to 52.7%. At the task level, at least one variant verifies for 49 of 73 tasks, a 67.1% success rate. These results show that task-equivalent implementations can differ substantially in verifiability and that implementation diversity helps find verification-friendly artifacts.