Proof2Silicon: Verified Hardware Synthesis

• Proof2Silicon is an end-to-end framework that converts natural language specifications into verified, synthesizable RTL code through RL-guided prompt repair, formal verification, and automated translation.
• The framework uses an RL-driven prompt repair mechanism that iteratively refines prompts based on formal verification feedback, significantly boosting verification success rates.
• Integrating Dafny-to-Python translation with PyLog-driven high-level synthesis, Proof2Silicon ensures hardware designs meet formal contracts and practical synthesis metrics.

Proof2Silicon is an end-to-end synthesis framework designed to generate correctness-by-construction hardware directly from natural language specifications. It introduces a multi-stage pipeline that leverages reinforcement learning (RL)-guided prompt repair, formal verification, and hardware synthesis to automate the translation of high-level requirements into synthesizable register-transfer level (RTL) code. The approach is notable for its integration of an RL-based feedback loop with an existing frozen LLM, thereby sidestepping the need for costly fine-tuning while systematically steering the code generation process toward formal correctness (Jha et al., 7 Sep 2025).

1. System Architecture and Workflow

Proof2Silicon incorporates several sequentially connected modules:

• RL-Guided Prompt Optimization (PREFACE): An RL agent operates on a Small LLM (SLM) to iteratively edit prompts to a frozen LLM. This loop is tightly coupled with a formal verifier and is specifically tailored to correct erroneous or unverifiable generated code.
• Formal Verification (Dafny): LLM-generated code, written in Dafny, is checked for satisfaction of specified contracts (pre/postconditions, invariants, etc.). Verifier-generated feedback is parsed and informs the RL policy.
• Automated Translation: Once a code candidate is formally verified, it is automatically translated to Python using Dafny's Python backend. Following a cleaning stage to remove Dafny-specific constructs, it is further decorated using PyLog for high-level synthesis compatibility.
• Hardware Synthesis: The PyLog-augmented Python is compiled to synthesizable HLS C, which is then ingested by Vivado HLS to produce RTL, enabling hardware implementation on FPGA platforms.

This integrated system bridges the entire pathway from natural-language specifications (τ) to formally verified, synthesizable silicon.

2. Reinforcement Learning-Driven Prompt Repair

Central to Proof2Silicon is the reinforcement learning methodology for iterative prompt repair:

• State Definition: Each RL state sₜ encapsulates the current prompt, the generated candidate code, and verifier-produced error trace.
• Actions: The RL agent proposes token-level prompt edits (Δpₜ) based on explicit verifier feedback.
• Reward Structure: A positive reward (+R_succ) is issued upon successful verification (eₜ+₁ = 0). Otherwise, the agent accrues a negative reward proportional to the new error count and an additional fixed penalty for empty outputs:

$$R(s_t, a_t) = \begin{cases} +R_\mathrm{succ} & \text{if } e_{t+1} = 0 \ -\alpha \cdot e_{t+1} - \beta & \text{otherwise} \end{cases}$$

with $\alpha = 0.2$, $\beta = 0.5$.

• Policy Optimization: The RL loop employs Proximal Policy Optimization (PPO). Actor and critic losses are optimized as:

$$L_{\text{actor}}(\theta) = -\mathbb{E}_t\left[\min(r_t(\theta) \hat{A}_t, \text{clip}(r_t(\theta), 1-\epsilon, 1+\epsilon)\hat{A}_t)\right]$$

$$L_{\text{critic}}(\phi) = \mathbb{E}_t\left[(V_\phi(s_t) - G_t)^2\right]$$

where $\hat{A}_t$ is the advantage estimate and $G_t$ is the observed return.

This RL mechanism allows frozen LLMs to be adaptively guided toward verified code outputs through sequential, verifier-informed prompt edits.

3. Formal Verification and Program Translation Pipeline

Upon verifier acceptance, the following automated steps occur:

• Dafny-to-Python Translation: Verified Dafny code is translated into Python using the Dafny compiler (e.g., dafny build --target:py verified.dfy). This preserves code correctness with respect to the original formal contracts.
• Code Sanitation: An automated script removes Dafny runtime imports, wrappers, and special mathematical constructs, replacing them with standard Python or NumPy equivalents. This ensures that the code becomes suitable for PyLog-driven transformation.
• High-Level Synthesis Preparation: The sanitized Python code is decorated with PyLog synthesizability hints (e.g., memory attributes, pipeline/unroll pragmas). Numerical types are resolved to explicit NumPy types (e.g., np.int32).
• Synthesis Flow: PyLog compiles the decorated Python to synthesizable HLS C. Vivado HLS then performs RTL synthesis, reporting resource utilization (LUTs, FFs, DSPs), timing, latency, and power metrics.

The pipeline is robust but recognizes that some Dafny-to-Python transformations may fail if the code includes unsupported constructs such as recursion or dynamic arrays, resulting in an overview gap.

4. Empirical Results and Benchmarking

The system's efficacy is validated on a suite of 100 tasks sampled from the DafnyBench benchmark:

• Verification Success:
  • RL-guided prompt repair provides up to a 21% improvement in formal verification pass rates across assessed LLMs compared to static or unoptimized prompting.
  • For example, ChatGPT-4o saw a baseline verification rate rise from 25% to 36% using untrained RL and further to 50% with fully trained RL-informed prompt repair.
• Hardware Synthesis Success:
  • For Gemini-2-Flash, 72% of verified Dafny tasks were successfully synthesized to RTL via the PyLog and Vivado HLS flow.
  • Synthesis resource utilization is reported, with representative kernels (e.g., Cube, Triangle Number) executing within practical latency and hardware resource limits.
• Resource Metrics:
  • Typical Vivado HLS flows (kernel synthesis) complete in 32–34 seconds and utilize approximately 680–705 MB of memory, supporting scalability.

Empirical training curves demonstrate convergence in policy/value losses and monotonic reward improvement across 2000 episodes.

5. Impact, Significance, and Technical Challenges

Proof2Silicon advances LLM-driven hardware synthesis with correctness guarantees through several key features:

• Bridging Software and Hardware: It closes the loop between high-level software specifications (in natural language), formal software verification, and practical silicon realization—an essential step for safety-critical hardware development.
• Scalable, Model-Agnostic RL Guidance: The use of RL-guided prompt repair allows the same frozen LLM to be repurposed for formally verified code generation across codebases and hardware targets, sidestepping costly retraining or model customization.
• Correctness-by-Construction: By embedding formal verification in the inner loop, only code guaranteed to meet pre/postconditions and invariants passes to downstream synthesis, minimizing risk in hardware generation.
• Practical Automation: The system demonstrates robust, scalable synthesis for a large task set, with feasible end-to-end resource requirements for pipeline operation.

Primary technical challenges identified include the translation limitations between Dafny and Python/C, the compatibility of LLM-generated code with synthesis tools, and the potential for further optimization if RTL performance metrics are included in the RL reward structure.

6. Future Directions

Several avenues for enhancement are outlined:

• Refining Translation for Synthesizability: Automatically constrain code generation and translation to exclude constructs unsupported by PyLog/HLS (e.g., dynamic data structures or recursion), increasing the proportion of successful RTL syntheses.
• Hardware-Aware Prompt Repair: Extend the RL reward beyond verification to include hardware-aware fitness metrics such as area, latency, and throughput as reported by HLS tools, enabling multi-objective prompt optimization.
• Benchmark and Dataset Expansion: Develop larger and more varied benchmarks to cover a broader set of program semantics and hardware design patterns, evaluating generalizability.
• EDA Toolchain Integration: Enable deeper coupling with additional electronic design automation tools for further design space exploration and downstream optimizations.
• Full-Stack End-to-End Learning: Pursue joint co-optimization where RL, formal verification, translation, and synthesis are more tightly integrated, potentially lowering failure rates and boosting synthesis rates.

These aims recognize the current limitations while charting a clear pathway toward a more comprehensive, formally correct, LLM-driven hardware synthesis ecosystem.

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Proof2Silicon demonstrates a robust method for end-to-end hardware synthesis from natural language, leveraging RL-driven prompt repair and formal verification to generate correctness-by-construction RTL, and sets a technical benchmark for future developments in automated high-assurance hardware generation via LLMs (Jha et al., 7 Sep 2025).