pith. sign in

arxiv: 2606.21451 · v1 · pith:A4MNMDH2new · submitted 2026-06-19 · 💻 cs.AR

Closing the Loop on LLM-Generated RTL Assertions with Quality-Aware Formal Verification

Ramesh Krishnamurthy , Danial Chitnis , Themis Prodromakis This is my paper

Pith reviewed 2026-06-26 12:50 UTC · model grok-4.3

classification 💻 cs.AR
keywords LLM-generated assertionsRTL formal verificationmutation-guided refinementsolver selectioncausal narrative synthesisquality-aware verificationformal property checking
0
0 comments X

The pith

A quality-aware loop refines LLM-generated assertions for RTL designs by rejecting weak properties, adapting solvers, and explaining failures from traces.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a framework that closes the loop on assertions produced by large language models for register transfer level hardware. It adds three steps: mutation-guided refinement to discard vacuous properties or ones that miss faulty behavior, selection of the best SMT solver based on design structure to stabilize runtimes, and synthesis of causal narratives from counterexample traces. These steps target the problems of assertions passing for incorrect reasons, highly variable proof costs, and difficult-to-interpret failures. A sympathetic reader would see this as shifting focus from generation alone to iterative quality improvement, making formal verification more usable in practice.

Core claim

The framework combines mutation-guided refinement to reject weak assertions including vacuous ones and those that fail to distinguish faulty behaviour, a solver-selection stage that chooses among candidate SMT backends using RTL structure, and causal narrative synthesis to explain why a proof failed. Across diverse RTL designs this improves confidence in generated assertions, reduces runtime variability over fixed-solver choices, and produces failure explanations grounded in the counterexample trace.

What carries the argument

The quality-aware closure loop that integrates mutation-guided refinement for weak-assertion rejection, RTL-structure-based solver selection, and causal narrative synthesis from counterexamples.

If this is right

  • Assertions become more likely to be non-vacuous and capable of distinguishing faulty behavior.
  • Formal proof runtimes exhibit lower variation when the solver is chosen according to RTL structure.
  • Failure reports provide explanations directly traceable to specific counterexample traces.
  • The practical bottleneck moves from assertion generation to quality-aware closure in LLM-assisted flows.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar quality loops could be tested on assertion generation for software or protocol verification.
  • The approach implies that combining multiple solvers with structure-based selection may generalize beyond the evaluated designs.
  • Engineers might reduce manual assertion review if the refinement step consistently filters low-value properties.

Load-bearing premise

Mutation-guided refinement can reliably reject weak assertions without introducing new false negatives or excessive computational overhead on the target RTL designs.

What would settle it

Applying the framework to a fresh set of RTL designs and finding that weak assertions are not rejected at higher rates than baseline or that runtime variability increases would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.21451 by Danial Chitnis, Ramesh Krishnamurthy, Themis Prodromakis.

Figure 1
Figure 1. Figure 1: The proposed quality-aware verification loop. The initial harness stage is shown only as a bootstrap. Solver selection is computed once from RTL [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustrative MGR refinement trajectories for UART [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Large language model (LLM) based assertion generation is making formal verification more accessible for Register Transfer Level (RTL) designs, but three practical issues remain. Generated properties can pass for the wrong reason, proof cost can vary widely from one design to another, and failing traces are hard to interpret. This paper presents a lightweight, open-source framework that addresses these issues in one loop. Our method combines mutation-guided refinement to reject weak assertions, including vacuous ones and those that fail to distinguish faulty behaviour, a solver-selection stage that chooses among candidate Satisfiability Modulo Theories (SMT) backends using RTL structure, and causal narrative synthesis to explain why a proof failed. Across diverse RTL designs, the framework improves confidence in generated assertions, reduces runtime variability over fixed-solver choices, and produces failure explanations that remain grounded in the counterexample trace. The results suggest that quality-aware closure, rather than assertion generation alone, is the missing step for practical LLM-assisted formal verification.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper presents a lightweight open-source framework that closes the loop on LLM-generated RTL assertions via three components: mutation-guided refinement to reject weak/vacuous assertions and those failing to distinguish faulty behavior, RTL-structure-based selection among SMT solvers to reduce runtime variability, and causal narrative synthesis to ground failure explanations in counterexample traces. The central claim is that this quality-aware approach improves assertion confidence, stabilizes performance across designs, and yields interpretable results, making it the missing step for practical LLM-assisted formal verification.

Significance. If the experimental results hold, the work has moderate significance for hardware verification and formal methods communities. The integration of mutation-based filtering, adaptive solver choice, and trace-grounded explanations directly targets practical barriers to LLM use in RTL, and the open-source release supports reproducibility and community extension. Credit is due for framing the problem as a closed-loop engineering task rather than isolated generation.

major comments (2)
  1. [framework description / mutation-guided refinement] Mutation-guided refinement (framework description): the central claim requires that the chosen mutations and acceptance criteria reliably reject vacuous assertions and those failing to distinguish faulty behaviour without introducing false negatives or excessive overhead; no formal coverage argument or empirical demonstration that the operator set is sufficient across arbitrary RTL designs is supplied, and this step is load-bearing because solver selection and narrative synthesis operate only on the surviving assertions.
  2. [Abstract] Abstract and results sections: the claim of improvements 'across diverse RTL designs' is unsupported by any quantitative metrics, error bars, dataset sizes, or baseline comparisons in the provided abstract; without these, it is impossible to assess whether the data actually supports the stated gains in confidence and runtime stability.
minor comments (1)
  1. The abstract introduces 'quality-aware closure' without a concise definition; a one-sentence gloss in the introduction would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and for recognizing the practical contributions of the closed-loop framework. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [framework description / mutation-guided refinement] Mutation-guided refinement (framework description): the central claim requires that the chosen mutations and acceptance criteria reliably reject vacuous assertions and those failing to distinguish faulty behaviour without introducing false negatives or excessive overhead; no formal coverage argument or empirical demonstration that the operator set is sufficient across arbitrary RTL designs is supplied, and this step is load-bearing because solver selection and narrative synthesis operate only on the surviving assertions.

    Authors: We agree that mutation-guided refinement is load-bearing for the overall approach. The manuscript reports empirical results across the evaluated RTL designs showing effective rejection of vacuous and non-distinguishing assertions with manageable overhead. However, no formal coverage argument for the mutation operator set across arbitrary designs is provided, as the technique is presented as a practical, heuristic method rather than a theoretically complete one. We will revise the framework description to add explicit discussion of the operator rationale, observed behavior on the tested designs, and acknowledged limitations regarding generality. revision: yes

  2. Referee: [Abstract] Abstract and results sections: the claim of improvements 'across diverse RTL designs' is unsupported by any quantitative metrics, error bars, dataset sizes, or baseline comparisons in the provided abstract; without these, it is impossible to assess whether the data actually supports the stated gains in confidence and runtime stability.

    Authors: The abstract is intentionally concise and therefore omits specific quantitative details. The results section supplies the supporting metrics, dataset sizes, and baseline comparisons. To improve clarity, we will revise the abstract to include concise quantitative highlights (e.g., number of designs, observed improvements in assertion acceptance rate and runtime stability) drawn from the existing results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; descriptive engineering framework with no derivations or self-referential reductions

full rationale

The paper presents a practical engineering framework combining mutation-guided refinement, solver selection based on RTL structure, and causal narrative synthesis for LLM-generated assertions. No equations, fitted parameters, or mathematical derivations appear in the provided text. Claims rest on empirical results across designs rather than any self-definition, fitted-input prediction, or load-bearing self-citation chain. The work is self-contained as a methodology description without reductions of outputs to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical model is presented; the contribution is an applied framework. No free parameters, axioms, or invented entities are introduced.

pith-pipeline@v0.9.1-grok · 5705 in / 1077 out tokens · 23029 ms · 2026-06-26T12:50:26.054216+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

23 extracted references · 7 canonical work pages

  1. [1]

    Specllm: Exploring generation and review of VLSI design specification with large language model,

    M. Li, W. Fang, Q. Zhang, and Z. Xie, “Specllm: Exploring generation and review of VLSI design specification with large language model,”CoRR, vol. abs/2401.13266, 2024. [Online]. Available: https://doi.org/10.48550/arXiv.2401.13266

    work page doi:10.48550/arxiv.2401.13266 2024

  2. [2]

    Assertllm: Generating hardware verification assertions from design specifications via multi-llms,

    Z. Yan, W. Fang, M. Li, M. Li, S. Liu, Z. Xie, and H. Zhang, “Assertllm: Generating hardware verification assertions from design specifications via multi-llms,” inProceedings of the 30th Asia and South Pacific Design Automation Conference, ASPDAC 2025, Tokyo, Japan, January 20-23, 2025, Y . Nakamura and Y . Wang, Eds. ACM, 2025, pp. 614–621. [Online]. Ava...

    work page doi:10.1145/3658617.3697756 2025

  3. [3]

    Assertionforge: Enhancing formal verification assertion generation with structured representation of specifications and RTL,

    Y . Bai, G. B. Hamad, S. Suhaib, and H. Ren, “Assertionforge: Enhancing formal verification assertion generation with structured representation of specifications and RTL,”CoRR, vol. abs/2503.19174,

    work page arXiv

  4. [4]

    Assertionforge: Enhancing formal verification assertion generation with structured representation of specifications and RTL,

    [Online]. Available: https://doi.org/10.48550/arXiv.2503.19174

    work page doi:10.48550/arxiv.2503.19174

  5. [5]

    Hardware design and verification with large language models: A literature survey, challenges, and open issues,

    M. Abdollahi, M. Dargahi, M. Rashidian, M. Shalan, and R. Karri, “Hardware design and verification with large language models: A literature survey, challenges, and open issues,”Electronics, vol. 14, no. 2, p. 265, 2025

    2025

  6. [6]

    Hey AI, generate me a hardware code! agentic AI-based hardware design & verification,

    D. N. Gadde, K. K. Radhakrishna, V . N. Viswambharan, A. Kumar, D. Lettnin, W. Kunz, and S. Simon, “Hey AI, generate me a hardware code! agentic AI-based hardware design & verification,” inProceedings of the 38th SBC/SBMicro/IEEE Symposium on Integrated Circuits and Systems Design (SBCCI), 2025

    2025

  7. [7]

    Efficient detection of vacuity in temporal model checking,

    I. Beer, S. Ben-David, C. Eisner, and Y . Rodeh, “Efficient detection of vacuity in temporal model checking,” inProceedings of the 12th International Conference on Computer Aided Verification (CAV), ser. LNCS, vol. 1855. Springer, 2001

    2001

  8. [8]

    Machsmt: A machine learning-based algorithm selector for SMT solvers,

    J. Scott, A. Niemetz, M. Preiner, S. Nejati, and V . Ganesh, “Machsmt: A machine learning-based algorithm selector for SMT solvers,” inTools and Algorithms for the Construction and Analysis of Systems, ser. Lecture Notes in Computer Science, J. F. Groote and K. G. Larsen, Eds., vol. 12652. Springer, 2021, pp. 303–325

    2021

  9. [9]

    Btor2-select: Machine learning based algorithm selection for hardware model check- ing,

    Z. Lu, P. Chien, N. Lee, A. Gurfinkel, and V . Ganesh, “Btor2-select: Machine learning based algorithm selection for hardware model check- ing,” inComputer Aided Verification, ser. Lecture Notes in Computer Science, vol. 15931. Springer, 2025

    2025

  10. [10]

    Spec2assertion: Automatic pre-RTL asser- tion generation by LLMs with progressive regularization,

    F. Wu, E. Pan, R. Kande, M. Quinn, A. Tyagi, D. K. Houngninou, J. Rajendran, and J. Hu, “Spec2assertion: Automatic pre-RTL asser- tion generation by LLMs with progressive regularization,”CoRR, vol. abs/2505.07995, 2025

    work page arXiv 2025

  11. [11]

    Deepassert: An LLM-aided verification framework with fine-grained assertion gen- eration for modules with extracted module specifications,

    Y . Wang, J. Zhou, H. Lyu, Z. Chao, T. Wang, and H. Li, “Deepassert: An LLM-aided verification framework with fine-grained assertion gen- eration for modules with extracted module specifications,”CoRR, vol. abs/2509.14668, 2025

    work page arXiv 2025

  12. [12]

    LLM-guided formal verification coupled with mutation testing,

    M. Hassan, S. Ahmadi-Pour, K. Qayyum, C. K. Jha, and R. Drechsler, “LLM-guided formal verification coupled with mutation testing,” in Proceedings of the Design, Automation and Test in Europe Conference (DATE), 2024, pp. 1–2

    2024

  13. [13]

    Saarthi: The first AI formal verification engineer,

    A. Kumar, D. N. Gadde, K. K. Radhakrishna, and D. Lettnin, “Saarthi: The first AI formal verification engineer,”CoRR, vol. abs/2409.06766, 2024

    work page arXiv 2024

  14. [14]

    Yosys-a free verilog synthesis suite,

    C. Wolf, J. Glaser, and J. Kepler, “Yosys-a free verilog synthesis suite,” inProceedings of the 21st Austrian Workshop on Microelectronics (Austrochip), vol. 97, 2013, pp. 1–6

    2013

  15. [15]

    An analysis and survey of the development of mutation testing,

    Y . Jia and M. Harman, “An analysis and survey of the development of mutation testing,”IEEE Transactions on Software Engineering, vol. 37, no. 5, pp. 649–678, 2011

    2011

  16. [16]

    Explaining counterexamples using causality,

    I. Beer, S. Ben-David, H. Chockler, A. Orni, and R. Trefler, “Explaining counterexamples using causality,” inComputer Aided Verification, ser. Lecture Notes in Computer Science, vol. 6174. Springer, 2010, pp. 94–108

    2010

  17. [17]

    A user study for evaluation of formal verification results and their explanation at bosch,

    A. P. Kaleeswaran, A. Nordmann, T. V ogel, and L. Grunske, “A user study for evaluation of formal verification results and their explanation at bosch,”Empirical Software Engineering, vol. 28, no. 125, 2023

    2023

  18. [18]

    Yices 2.2,

    B. Dutertre, “Yices 2.2,” inComputer Aided Verification - 26th Inter- national Conference, CAV 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, Vienna, Austria, July 18–22, 2014. Proceedings, ser. Lecture Notes in Computer Science, A. Biere and R. Bloem, Eds., vol

    2014

  19. [19]

    Springer, 2014, pp. 737–744

    2014

  20. [20]

    Bitwuzla,

    A. Niemetz and M. Preiner, “Bitwuzla,” inComputer Aided Verification - 35th International Conference, CAV 2023, Paris, France, July 17–22, 2023, Proceedings, Part II, ser. Lecture Notes in Computer Science, C. Enea and A. Lal, Eds., vol. 13965. Springer, 2023, pp. 3–17

    2023

  21. [21]

    Z3: An efficient SMT solver,

    L. de Moura and N. Bjørner, “Z3: An efficient SMT solver,” inTools and Algorithms for the Construction and Analysis of Systems, TACAS 2008, ser. Lecture Notes in Computer Science, C. R. Ramakrishnan and J. Rehof, Eds., vol. 4963. Springer, 2008, pp. 337–340

    2008

  22. [22]

    cvc5: A versatile and industrial-strength SMT solver,

    H. Barbosa, C. W. Barrett, M. Brain, G. Kremer, H. Lachnitt, M. Mann, A. Mohamed, M. Mohamed, A. Niemetz, A. N ¨otzli, A. Ozdemir, M. Preiner, A. Reynolds, Y . Sheng, C. Tinelli, and Y . Zohar, “cvc5: A versatile and industrial-strength SMT solver,” inTools and Algorithms for the Construction and Analysis of Systems - 28th International Con- ference, TACA...

    2022

  23. [23]

    Symbolic model checking without BDDs,

    A. Biere, A. Cimatti, E. M. Clarke, and Y . Zhu, “Symbolic model checking without BDDs,” inTools and Algorithms for the Construction and Analysis of Systems (TACAS), ser. Lecture Notes in Computer Science, vol. 1579. Springer, 1999, pp. 193–207

    1999