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International Conference on Current Trends in Theory and Practice of Informatics

SOFSEM 2019: SOFSEM 2019: Theory and Practice of Computer Science pp 206–220Cite as

Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11376))

Abstract

We identify difference-bound set constraints (DBS), an analogy of difference-bound arithmetic constraints for sets. DBS can express not only set constraints but also arithmetic constraints over set elements. We integrate DBS into separation logic with linearly compositional inductive predicates, obtaining a logic thereof where set data constraints of linear data structures can be specified. We show that the satisfiability of this logic is decidable. A crucial step of the decision procedure is to compute the transitive closure of DBS-definable set relations, to capture which we propose an extension of quantified set constraints with Presburger Arithmetic (RQSPA). The satisfiability of RQSPA is then shown to be decidable by harnessing advanced automata-theoretic techniques.

Partially supported by the NSFC grants (No. 61472474, 61572478, 61872340), UK EPSRC grant (EP/P00430X/1), and the INRIA-CAS joint research project VIP.

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Notes

  1. 1.

    This shall be usually referred to as “transitive closure of \(\mathcal {DBS}\)” to avoid clumsiness.

  2. 2.

    The operators < and > can be seen as abbreviations, for instance, \(x < y\) is equivalent to \(x \le y -1\), which will be used later on as well.

  3. 3.

    An unrestricted extension of quantified set constraints with Presburger Arithmetic is undecidable, as shown in [6].

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Author information

Authors and Affiliations

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

    Chong Gao & Zhilin Wu

  2. University of Chinese Academy of Sciences, Beijing, China

    Chong Gao

  3. Department of Computer Science and Information Systems, Birkbeck, University of London, London, UK

    Taolue Chen

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  1. Chong Gao
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  2. Taolue Chen
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  3. Zhilin Wu
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Correspondence to Zhilin Wu .

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Editors and Affiliations

  1. University of Genoa, Genoa, Italy

    Barbara Catania

  2. Comenius University, Bratislava, Slovakia

    Rastislav Královič

  3. Poznań University of Technology, Poznań, Poland

    Jerzy Nawrocki

  4. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

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Gao, C., Chen, T., Wu, Z. (2019). Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints. In: Catania, B., Královič, R., Nawrocki, J., Pighizzini, G. (eds) SOFSEM 2019: Theory and Practice of Computer Science. SOFSEM 2019. Lecture Notes in Computer Science(), vol 11376. Springer, Cham. https://doi.org/10.1007/978-3-030-10801-4_17

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