# Worst-Case Symbolic Constraints Analysis and Generalisation with Large Language Models

arXiv: https://arxiv.org/abs/2506.08171 · HTML: https://mlsanity.com/paper/2506.08171/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 13 of 13)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Provers](https://mlsanity.com/paper/2205.10893/) (2022)
- [ChatGPT for Vulnerability Detection, Classification, and Repair: How Far Are We?](https://mlsanity.com/paper/2310.09810/) (2023)
- [AI-assisted coding: Experiments with GPT-4](https://mlsanity.com/paper/2304.13187/) (2023)
- [A New Era in Software Security: Towards Self-Healing Software via Large Language Models and Formal Verification](https://mlsanity.com/paper/2305.14752/) (2023)
- [Towards Finding Longer Proofs](https://mlsanity.com/paper/1905.13100/) (2019)
- [Badger: Complexity Analysis with Fuzzing and Symbolic Execution](https://mlsanity.com/paper/1806.03283/) (2018)

## Built on by (most cited first, 1 of 1)

- [Can Large Language Models Reason About Complex Execution Paths? An Empirical Study on Python](https://mlsanity.com/paper/2511.18288/) (2025)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated strong performance on coding tasks such as generation, completion and repair, but their ability to handle complex symbolic reasoning over code still remains underexplored. We introduce the task of worst-case symbolic constraints analysis, which requires inferring the symbolic constraints that characterise worst-case program executions; these constraints can be solved to obtain inputs that expose performance bottlenecks or denial-of-service vulnerabilities in software systems. We show that even state-of-the-art LLMs (e.g., GPT-5) struggle when applied directly on this task. To address this challenge, we propose WARP, an innovative neurosymbolic approach that computes worst-case constraints on smaller concrete input sizes using existing program analysis tools, and then leverages LLMs to generalise these constraints to larger input sizes. Concretely, WARP comprises: (1) an incremental strategy for LLM-based worst-case reasoning, (2) a solver-aligned neurosymbolic framework that integrates reinforcement learning with SMT (Satisfiability Modulo Theories) solving, and (3) a curated dataset of symbolic constraints. Experimental results show that WARP consistently improves performance on worst-case constraint reasoning. Leveraging the curated constraint dataset, we use reinforcement learning to fine-tune a model, WARP-1.0-3B, which significantly outperforms size-matched and even larger baselines. These results demonstrate that incremental constraint reasoning enhances LLMs' ability to handle symbolic reasoning and highlight the potential for deeper integration between neural learning and formal methods in rigorous program analysis.