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Empirically Scalable Invariant Generation Leveraging Divide-and-Conquer with Pruning

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Theoretical Aspects of Software Engineering (TASE 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14777))

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Abstract

Invariant generation is a critical task in program verification. Literature highlights Farkas’ Lemma as a principal sound and complete framework for proactively generating tight invariants in constraint-solving. Recent advances have identified the conversion from CNF to DNF as a major bottleneck, leading to a combinatorial explosion. In this study, we introduce an optimized algorithm to address the combinatorial explosion by trading off space for time-efficiency. Our approach employs two key strategies to boost speed. First, we apply a divide-and-conquer strategy to decompose a complex problem into smaller, more manageable subproblems that can be solved quickly and in parallel. Second, we intelligently apply a pruning strategy in two ways, navigating the depth-first search process to avoid unnecessary checks. These improvements maintain the accuracy and speed up the analysis. The experiments indicate that our approach outperforms the state-of-the-art, demonstrating significant speed improvements. With this solution, we bring a significant advance in accelerating invariant generation with Farkas’ Lemma.

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Acknowledgement

This work is supported by the National Natural Science Foundation of China Grant No. 61872232.

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Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Hongming Liu & Guoqiang Li

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  1. Hongming Liu
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  2. Guoqiang Li
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Correspondence to Guoqiang Li .

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  1. National University of Singapore, Singapore, Singapore

    Wei-Ngan Chin

  2. Shenzhen University, Guangdong, China

    Zhiwu Xu

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Liu, H., Li, G. (2024). Empirically Scalable Invariant Generation Leveraging Divide-and-Conquer with Pruning. In: Chin, WN., Xu, Z. (eds) Theoretical Aspects of Software Engineering. TASE 2024. Lecture Notes in Computer Science, vol 14777. Springer, Cham. https://doi.org/10.1007/978-3-031-64626-3_19

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  • DOI: https://doi.org/10.1007/978-3-031-64626-3_19

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