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Array Theory of Bounded Elements and its Applications

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Abstract

We investigate a first-order array theory of bounded elements. This theory has rich expressive power that allows free use of quantifiers. By reducing to weak second-order logic with one successor (WS1S), we show that the proposed array theory is decidable. Then two natural extensions to the new theory are shown to be undecidable. A translation-based decision procedure for this theory is implemented, and is shown applicable to program verification.

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Authors and Affiliations

  1. School of Software, Tsinghua University, Beijing, 100084, China

    Min Zhou, Fei He, Ming Gu & Jiaguang Sun

  2. Tsinghua National Laboratory for Information Science and Technology, Beijing, China

    Min Zhou, Fei He, Ming Gu & Jiaguang Sun

  3. Key Laboratory for Information System Security, MOE, Beijing, China

    Min Zhou, Fei He, Ming Gu & Jiaguang Sun

  4. Academia Sinica, Taipei, Taiwan

    Bow-Yaw Wang

Authors
  1. Min Zhou
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  2. Fei He
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  3. Bow-Yaw Wang
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  4. Ming Gu
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  5. Jiaguang Sun
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Correspondence to Min Zhou.

Additional information

This work was supported by the Chinese National 973 Plan under grant No. 2010CB328003, the NSF of China under grants No. 61272001, 60903030, 91218302, the Chinese National Key Technology R&D Program under grant No. SQ2012BAJY4052, the Tsinghua University Initiative Scientific Research Program, and the National Science Council of Taiwan projects No. NSC101-2221-E-001-006-, NSC102-2221-E-001-017-.

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Zhou, M., He, F., Wang, BY. et al. Array Theory of Bounded Elements and its Applications. J Autom Reasoning 52, 379–405 (2014). https://doi.org/10.1007/s10817-013-9293-6

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