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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…

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

Loop invariants are software properties that hold before and after every iteration of a loop. As such, invariants provide inductive arguments that are key in automating the verification of program loops. The problem of generating loop…

Logic in Computer Science · Computer Science 2023-05-25 George Kenison , Laura Kovács , Anton Varonka

Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information…

Machine Learning · Computer Science 2026-05-08 Hua-Dong Xiong

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

Large Language Models (LLMs) have demonstrated remarkable performance in code completion. However, the training data used to develop these models often contain a significant amount of buggy code. Yet, it remains unclear to what extent these…

Software Engineering · Computer Science 2025-03-17 Liwei Guo , Sixiang Ye , Zeyu Sun , Xiang Chen , Yuxia Zhang , Bo Wang , Jie M. Zhang , Zheng Li , Yong Liu

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…

Large Language Models (LLMs) have successfully been applied to code generation tasks, raising the question of how well these models understand programming. Typical programming languages have invariances and equivariances in their semantics…

Computation and Language · Computer Science 2023-05-26 Antonio Valerio Miceli-Barone , Fazl Barez , Ioannis Konstas , Shay B. Cohen

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

Large Language Models(LLMs) have been actively integrated into modern software systems as critical components. LLM-in-the-loop vulnerabilities, where vulnerabilities are introduced by LLMs and their dependent downstream components, such as…

Software Engineering · Computer Science 2026-05-29 Yujie Ma , Jialin Rong , Chenxi Yang , Lili Quan , Xiaofei Xie , Yongqiang Lyu , Qiang Hu

The synthesis of inductive loop invariants is a critical bottleneck in automated program verification. While Large Language Models (LLMs) show promise in mitigating this issue, they often fail on hard instances, generating invariants that…

Machine Learning · Computer Science 2026-03-17 Ido Pinto , Yizhak Yisrael Elboher , Haoze Wu , Nina Narodytska , Guy Katz

Automated program verification has always been an important component of building trustworthy software. While the analysis of real-world programs remains a theoretical challenge, the automation of loop invariant analysis has effectively…

Software Engineering · Computer Science 2025-09-17 Ruibang Liu , Minyu Chen , Ling-I Wu , Jingyu Ke , Guoqiang Li

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

Large Language Models (LLMs) have emerged as a groundbreaking technology with their unparalleled text generation capabilities across various applications. Nevertheless, concerns persist regarding the accuracy and appropriateness of their…

Computation and Language · Computer Science 2024-03-15 Jie Huang , Xinyun Chen , Swaroop Mishra , Huaixiu Steven Zheng , Adams Wei Yu , Xinying Song , Denny Zhou

We propose a novel framework that provides constructive feedback to an LLM in the "guess-and-check" paradigm by formally verifying its own thinking process and detecting local reasoning errors. We apply this framework to the loop invariant…

Programming Languages · Computer Science 2026-05-19 Tianchi Li , Zhenyu Yan , Junhao Liu , Peng Di , Xin Zhang

Loop invariants are properties of a program loop that hold both before and after each iteration of the loop. They are often used to verify programs and ensure that algorithms consistently produce correct results during execution.…

Symbolic Computation · Computer Science 2026-01-08 Erdenebayar Bayarmagnai , Fatemeh Mohammadi , Rémi Prébet

Large Language Models (LLMs) have become powerful tools for automated code generation. However, these models often overlook critical security practices, which can result in the generation of insecure code that contains…

Software Engineering · Computer Science 2025-07-01 Hao Yan , Swapneel Suhas Vaidya , Xiaokuan Zhang , Ziyu Yao

Loop invariants are fundamental for reasoning about the correctness of iterative algorithms. However, deriving suitable invariants remains a challenging and often manual task, particularly for complex programs. In this paper, we introduce…

Programming Languages · Computer Science 2026-01-06 Mingxiu Wang , Jiawei Wang , Xiao Cheng

Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…

Symbolic Computation · Computer Science 2024-05-16 Erdenebayar Bayarmagnai , Fatemeh Mohammadi , Rémi Prébet

Software verification has emerged as a key concern for ensuring the continued progress of information technology. Full verification generally requires, as a crucial step, equipping each loop with a "loop invariant". Beyond their role in…

Software Engineering · Computer Science 2014-01-14 Carlo A. Furia , Bertrand Meyer , Sergey Velder
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