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Discovering non-terminating inputs for multi-path polynomial programs

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Abstract

This paper investigates the termination problems of multi-path polynomial programs (MPPs) with equational loop guards. To establish sufficient conditions for termination and nontermination simultaneously, the authors propose the notion of strong/weak non-termination which under/over-approximates non-termination. Based on polynomial ideal theory, the authors show that the set of all strong non-terminating inputs (SNTI) and weak non-terminating inputs (WNTI) both correspond to the real varieties of certain polynomial ideals. Furthermore, the authors prove that the variety of SNTI is computable, and under some sufficient conditions the variety of WNTI is also computable. Then by checking the computed SNTI and WNTI varieties in parallel, termination properties of a considered MPP can be asserted. As a consequence, the authors establish a new framework for termination analysis of MPPs.

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Authors and Affiliations

  1. Chongqing Key Laboratory of Automated Reasoning and Cognition, CIGIT, Chinese Academy of Sciences, Chongqing, 400714, China

    Jiang Liu & Hengjun Zhao

  2. Department of Computer Science and Technology, East China Normal University, Shanghai, 200241, China

    Ming Xu

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Naijun Zhan & Hengjun Zhao

Authors
  1. Jiang Liu
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  2. Ming Xu
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  3. Naijun Zhan
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  4. Hengjun Zhao
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Corresponding author

Correspondence to Hengjun Zhao.

Additional information

This research was supported by the National Basic Research Program of China under Grant No. 2014CB340700, the National Science and Technology Major Project of China under Grant No. 2012ZX01039-004, the National Natural Science Foundation of China under Grant Nos. 91118007, 11071273, 61202131, 11401218, cstc2012ggB40004, cstc2013jjys40001, SRFDP under Grant No. 20130076120010, the Open Project of Shanghai Key Laboratory of Trustworthy Computing under Grant No. 07dz22304201307, and West Light Foundation of Chinese Academy of Sciences.

This paper was recommended for publication by Editor LI Ziming.

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Liu, J., Xu, M., Zhan, N. et al. Discovering non-terminating inputs for multi-path polynomial programs. J Syst Sci Complex 27, 1286–1304 (2014). https://doi.org/10.1007/s11424-014-2145-6

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  • DOI: https://doi.org/10.1007/s11424-014-2145-6

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