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ESOP 2022: Programming Languages and Systems pp 57–84Cite as

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Foundations for Entailment Checking in Quantitative Separation Logic

Foundations for Entailment Checking in Quantitative Separation Logic

  • Kevin Batz  ORCID: orcid.org/0000-0001-8705-25649,
  • Ira Fesefeldt  ORCID: orcid.org/0000-0001-7837-26119,
  • Marvin Jansen9,
  • Joost-Pieter Katoen  ORCID: orcid.org/0000-0002-6143-19269,
  • Florian Keßler9,
  • Christoph Matheja  ORCID: orcid.org/0000-0001-9151-044110,11 &
  • …
  • Thomas Noll  ORCID: orcid.org/0000-0002-1865-17989 
  • Conference paper
  • Open Access
  • First Online: 29 March 2022

  • 2326 Accesses

  • 2 Citations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13240)

Abstract

Quantitative separation logic (QSL) is an extension of separation logic (SL) for the verification of probabilistic pointer programs. In QSL, formulae evaluate to real numbers instead of truth values, e.g., the probability of memory-safe termination in a given symbolic heap. As with SL, one of the key problems when reasoning with QSL is entailment: does a formula f entail another formula g?

We give a generic reduction from entailment checking in QSL to entailment checking in SL. This allows to leverage the large body of SL research for the automated verification of probabilistic pointer programs. We analyze the complexity of our approach and demonstrate its applicability. In particular, we obtain the first decidability results for the verification of such programs by applying our reduction to a quantitative extension of the well-known symbolic-heap fragment of separation logic.

This work is partially supported by the ERC AdG project 787914 FRAPPANT.

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Authors and Affiliations

  1. Software Modeling and Verification Group, RWTH Aachen University, Aachen, Germany

    Kevin Batz, Ira Fesefeldt, Marvin Jansen, Joost-Pieter Katoen, Florian Keßler & Thomas Noll

  2. Programming Methodology Group, ETH Zürich, Zürich, Switzerland

    Christoph Matheja

  3. Technical University of Denmark, Lyngby, Denmark

    Christoph Matheja

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Correspondence to Kevin Batz , Ira Fesefeldt , Joost-Pieter Katoen , Christoph Matheja or Thomas Noll .

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  1. National University of Singapore, Singapore, Singapore

    Ilya Sergey

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Batz, K. et al. (2022). Foundations for Entailment Checking in Quantitative Separation Logic. In: Sergey, I. (eds) Programming Languages and Systems. ESOP 2022. Lecture Notes in Computer Science, vol 13240. Springer, Cham. https://doi.org/10.1007/978-3-030-99336-8_3

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  • DOI: https://doi.org/10.1007/978-3-030-99336-8_3

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