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Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to…

Loop invariants are essential for proving the correctness of programs with loops. Developing loop invariants is challenging, and fully automatic synthesis cannot be guaranteed for arbitrary programs. Some approaches have been proposed to…

Logic in Computer Science · Computer Science 2025-08-04 Varun Bharti , Shashwat Jha , Dhruv Kumar , Pankaj Jalote

A loop invariant is a property of a loop that remains true before and after each execution of the loop. The identification of loop invariants is a critical step to support automated program safety assessment. Recent advancements in Large…

Software Engineering · Computer Science 2025-11-11 Mostafijur Rahman Akhond , Saikat Chakraborty , Gias Uddin

Large Language Models (LLMs) are showing remarkable performance in generating source code, yet the generated code often has issues like compilation errors or incorrect code. Researchers and developers often face wasted effort in…

Software Engineering · Computer Science 2026-03-26 Ravin Ravi , Dylan Bradshaw , Stefano Ruberto , Gunel Jahangirova , Valerio Terragni

Program verification is vital for ensuring software reliability, especially in the context of increasingly complex systems. Loop invariants, remaining true before and after each iteration of loops, are crucial for this verification process.…

Programming Languages · Computer Science 2024-06-10 Chang Liu , Xiwei Wu , Yuan Feng , Qinxiang Cao , Junchi Yan

Large language models (LLMs) are increasingly used for program verification, and yet little is known about \emph{how} they reason about program semantics during this process. In this work, we focus on abstract interpretation based-reasoning…

Machine Learning · Computer Science 2025-10-01 Jacqueline L. Mitchell , Brian Hyeongseok Kim , Chenyu Zhou , Chao Wang

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in…

The recent progress in large language models (LLMs), especially the invention of chain-of-thought prompting, has made it possible to automatically answer questions by stepwise reasoning. However, when faced with more complicated problems…

Artificial Intelligence · Computer Science 2023-10-06 Ning Miao , Yee Whye Teh , Tom Rainforth

Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…

Logic in Computer Science · Computer Science 2021-03-08 Andreas Humenberger , Laura Kovacs

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis.…

Formal Languages and Automata Theory · Computer Science 2023-11-27 Jianan Yao , Ziqiao Zhou , Weiteng Chen , Weidong Cui

Program verification relies on loop invariants, yet automatically discovering strong invariants remains a long-standing challenge. We investigate whether large language models (LLMs) can accelerate program verification by generating useful…

Programming Languages · Computer Science 2026-04-03 Anjiang Wei , Tianran Sun , Tarun Suresh , Haoze Wu , Ke Wang , Alex Aiken

Large Language Models (LLMs) have shown promising results in automating formal verification. However, existing approaches treat proof generation as a static, end-to-end prediction over source code, relying on limited verifier feedback and…

Programming Languages · Computer Science 2026-03-31 Jun Yang , Yuechun Sun , Yi Wu , Rodrigo Caridad , Yongwei Yuan , Jianan Yao , Shan Lu , Kexin Pei

Understanding a program's runtime reasoning behavior, meaning how intermediate states and control flows lead to final execution results, is essential for reliable code generation, debugging, and automated reasoning. Although large language…

Software Engineering · Computer Science 2025-12-02 Mohammad Abdollahi , Khandaker Rifah Tasnia , Soumit Kanti Saha , Jinqiu Yang , Song Wang , Hadi Hemmati

Large language models (LLMs) have demonstrated outstanding performance across various tasks, yet they still exhibit limitations such as hallucination, unfaithful reasoning, and toxic content. One potential approach to mitigate these issues…

Computation and Language · Computer Science 2024-07-19 Yuxuan Yao , Han Wu , Zhijiang Guo , Biyan Zhou , Jiahui Gao , Sichun Luo , Hanxu Hou , Xiaojin Fu , Linqi Song

Recent advances in Large Language Models (LLMs) have shown that their reasoning capabilities can be significantly improved through Reinforcement Learning with Verifiable Reward (RLVR), particularly in domains like mathematics and…

Large language models (LLMs) excel at zero-shot inference but continue to struggle with complex, multi-step reasoning. Recent methods that augment LLMs with intermediate reasoning steps such as Chain of Thought (CoT) and Program of Thought…

Computation and Language · Computer Science 2025-10-28 Adam Stein , Neelay Velingker , Mayur Naik , Eric Wong

Large language models (LLMs) have been shown to be capable of impressive few-shot generalisation to new tasks. However, they still tend to perform poorly on multi-step logical reasoning problems. Here we carry out a comprehensive evaluation…

Artificial Intelligence · Computer Science 2022-05-20 Antonia Creswell , Murray Shanahan , Irina Higgins

The dependence of Natural Language Processing (NLP) intelligent software on Large Language Models (LLMs) is increasingly prominent, underscoring the necessity for robustness testing. Current testing methods focus solely on the robustness of…

Software Engineering · Computer Science 2024-02-22 Mingxuan Xiao , Yan Xiao , Hai Dong , Shunhui Ji , Pengcheng Zhang

Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…

Logic in Computer Science · Computer Science 2017-08-25 G. W. Hamilton

Language Models (LMs) have shown impressive performance in various natural language tasks. However, when it comes to natural language reasoning, LMs still face challenges such as hallucination, generating incorrect intermediate reasoning…

Computation and Language · Computer Science 2023-10-20 Deepak Nathani , David Wang , Liangming Pan , William Yang Wang
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