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Making Rigorous Linear Programming Practical for Program Analysis

Authors: Tengbin Wang, Liqian Chen, Taoqing Chen, Guangsheng Fan, and Ji Wang

Published in: LIPIcs, Volume 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)


Abstract
Linear programming is a key technique for analysis and verification of numerical properties in programs, neural networks, etc. In particular, in program analysis based on abstract interpretation, many numerical abstract domains (such as Template Constraint Matrix, constraint-only polyhedra, etc.) are designed on top of linear programming. However, most state-of-the-art linear programming solvers use floating-point arithmetic in their implementations, leading to an approximate result that may be unsound. On the other hand, the solvers implemented using exact arithmetic are too costly. To this end, this paper focuses on advancing rigorous linear programming techniques based on floating-point arithmetic for building sound and efficient program analysis. Particularly, as a supplement to existing techniques, we present a novel rigorous linear programming technique based on Fourier-Mozkin elimination. On this basis, we implement a tool, namely, RlpSolver, combining our technique with existing techniques to lift effectiveness of rigorous linear programming in the scene of analysis and verification. Experimental results show that our technique is complementary to existing techniques, and their combination (RlpSolver) can achieve a better trade-off between cost and precision via heuristic rules.

Cite as

Tengbin Wang, Liqian Chen, Taoqing Chen, Guangsheng Fan, and Ji Wang. Making Rigorous Linear Programming Practical for Program Analysis. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 57:1-57:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{wang_et_al:LIPIcs.CP.2021.57,
  author =	{Wang, Tengbin and Chen, Liqian and Chen, Taoqing and Fan, Guangsheng and Wang, Ji},
  title =	{{Making Rigorous Linear Programming Practical for Program Analysis}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{57:1--57:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.57},
  URN =		{urn:nbn:de:0030-drops-153486},
  doi =		{10.4230/LIPIcs.CP.2021.57},
  annote =	{Keywords: Linear programming, rigorous linear programming, abstract interpretation, program analysis, Fourier-Mozkin elimination}
}
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