[Paper] TLA-Prover: Verifiable TLA+ Specification Synthesis via Preference-Optimized Low-Rank Adaptation

Source: arXiv - 2606.06133v1

Overview

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.

Key Contributions

This paper presents research in the following areas:

• cs.SE
• cs.AI
• cs.LG
• cs.LO

Methodology

Please refer to the full paper for detailed methodology.

Practical Implications

This research contributes to the advancement of cs.SE.

Authors

• Eric Spencer
• Arslan Bisharat
• Brian Ortiz
• Khushboo Bhadauria
• TaiNing Wang
• George K. Thiruvathukal
• Konstantin Laufer
• Mohammed Abuhamad

Paper Information

• arXiv ID: 2606.06133v1
• Categories: cs.SE, cs.AI, cs.LG, cs.LO
• Published: June 4, 2026
• PDF: Download PDF