{"ID":3083744,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-07T03:21:39.539466367Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.06133","arxiv_id":"2606.06133","title":"TLA-Prover: Verifiable TLA+ Specification Synthesis via Preference-Optimized Low-Rank Adaptation","abstract":"TLA+ is a formal specification language for verifying distributed systems and safety-critical protocols. Large language models (LLMs) frequently produce TLA+ specifications that fail the TLC model checker for semantic reasons. Across 25 LLMs, the best public baseline is 26.6% syntactic parse and 8.6% semantic model-check. We present TLA-Prover, a 20-billion-parameter model for TLA+ specification synthesis. Training combines supervised fine-tuning (SFT) on verified examples with repair-based group-relative policy optimization (GRPO). In the GRPO stage, the model learns to fix its own rejected specifications. We also train a direct preference optimization (DPO) variant from the same SFT checkpoint as an ablation. TLC provides the reward signal directly, with no learned reward model. Four tiers grade each output: Bronze (parses), Silver (no warnings), Gold (passes TLC), and Diamond. To reach Diamond, the model's correctness property is automatically altered in a small way; TLC must then detect a violation. If TLC still passes, the property was always-true and contributes nothing; the output fails Diamond. TLA-Prover reaches 9/30 (i.e. pass@1 = 30%) at both Gold and Diamond on a held-out 30-problem benchmark. This is roughly 3.5x the 8.6% untuned baseline. The DPO variant reaches 20% at Diamond. Gold and Diamond coincide at every checkpoint; this prevents the trivial-property failure mode.","short_abstract":"TLA+ is a formal specification language for verifying distributed systems and safety-critical protocols. Large language models (LLMs) frequently produce TLA+ specifications that fail the TLC model checker for semantic reasons. Across 25 LLMs, the best public baseline is 26.6% syntactic parse and 8.6% semantic model-che...","url_abs":"https://arxiv.org/abs/2606.06133","url_pdf":"https://arxiv.org/pdf/2606.06133v1","authors":"[\"Eric Spencer\",\"Arslan Bisharat\",\"Brian Ortiz\",\"Khushboo Bhadauria\",\"TaiNing Wang\",\"George K. Thiruvathukal\",\"Konstantin Laufer\",\"Mohammed Abuhamad\"]","published":"2026-06-04T13:17:06Z","proceeding":"cs.SE","tasks":"[\"cs.SE\",\"cs.AI\",\"cs.LG\",\"cs.LO\"]","methods":"[\"Large Language Model\",\"Language Model\"]","has_code":false}