research-article

A Decision Procedure for Guarded Separation Logic Complete Entailment Checking for Separation Logic with Inductive Definitions

Authors:

Christoph Matheja,

Florian ZulegerAuthors Info & Claims

ACM Transactions on Computational Logic, Volume 24, Issue 1

Article No.: 1, Pages 1 - 76

https://doi.org/10.1145/3534927

Published: 18 January 2023 Publication History

Abstract

We develop a doubly exponential decision procedure for the satisfiability problem of guarded separation logic—a novel fragment of separation logic featuring user-supplied inductive predicates, Boolean connectives, and separating connectives, including restricted (guarded) versions of negation, magic wand, and septraction. Moreover, we show that dropping the guards for any of the preceding connectives leads to an undecidable fragment.

We further apply our decision procedure to reason about entailments in the popular symbolic heap fragment of separation logic. In particular, we obtain a doubly exponential decision procedure for entailments between (quantifier-free) symbolic heaps with inductive predicate definitions of bounded treewidth (SL_btw)—one of the most expressive decidable fragments of separation logic. Together with the recently shown 2ExpTime-hardness for entailments in said fragment, we conclude that the entailment problem for SL_btw is 2ExpTime-complete—thereby closing a previously open complexity gap.

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Cited By

Saotome KNakazawa KKimura D(2024)Restriction on cut rule in cyclic-proof system for symbolic heapsTheoretical Computer Science10.1016/j.tcs.2024.1148541019(114854)Online publication date: Dec-2024
https://doi.org/10.1016/j.tcs.2024.114854
Bozec TPeltier NPetitjean QSighireanu M(2024)What Is Decidable in Separation Logic Beyond Progress, Connectivity and Establishment?Automated Reasoning10.1007/978-3-031-63501-4_9(157-175)Online publication date: 2-Jul-2024
https://doi.org/10.1007/978-3-031-63501-4_9

Index Terms

A Decision Procedure for Guarded Separation Logic Complete Entailment Checking for Separation Logic with Inductive Definitions
1. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Logic

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 24, Issue 1

January 2023

326 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/3579819

Editor:
Anuj Dawar
University of Cambridge, United Kingdom

Issue’s Table of Contents

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Association for Computing Machinery

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Publication History

Published: 18 January 2023

Online AM: 22 September 2022

Accepted: 30 April 2022

Revised: 25 November 2021

Received: 11 January 2021

Published in TOCL Volume 24, Issue 1

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Cited By

Saotome KNakazawa KKimura D(2024)Restriction on cut rule in cyclic-proof system for symbolic heapsTheoretical Computer Science10.1016/j.tcs.2024.1148541019(114854)Online publication date: Dec-2024
https://doi.org/10.1016/j.tcs.2024.114854
Bozec TPeltier NPetitjean QSighireanu M(2024)What Is Decidable in Separation Logic Beyond Progress, Connectivity and Establishment?Automated Reasoning10.1007/978-3-031-63501-4_9(157-175)Online publication date: 2-Jul-2024
https://doi.org/10.1007/978-3-031-63501-4_9

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