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Beyond Symbolic Heaps: Deciding Separation Logic With Inductive Definitions

19 pagesPublished: May 27, 2020

Abstract

Symbolic-heap separation logic with inductive definitions is a popular formalism for reasoning about heap-manipulating programs. The fragment SLIDbtw introduced by Iosif, Rogalewicz and Simacek, is one of the most expressive fragments with a decidable entailment problem. In recent work, we improved on the original decidability proof by providing a direct model-theoretic construction, obtaining a 2-Exptime upper bound. In this paper, we investigate separation logics built on top of the inductive definitions from SLIDbtw, i.e., logics that feature the standard Boolean and separation-logic operators. We give an almost tight delineation between decidability and undecidabilty. We establish the decidability of the satisfiability problem (in 2-Exptime) of a separation logic with conjunction, disjunction, separating conjunction and guarded forms of negation, magic wand, and septraction. We show that any further generalization leads to undecidabilty (under mild assumptions).

Keyphrases: decision procedure, separation logic, undecidability

In: Elvira Albert and Laura Kovacs (editors). LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 73, pages 390-408.

BibTeX entry
@inproceedings{LPAR23:Beyond_Symbolic_Heaps_Deciding,
  author    = {Jens Pagel and Florian Zuleger},
  title     = {Beyond Symbolic Heaps: Deciding Separation Logic With Inductive Definitions},
  booktitle = {LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Elvira Albert and Laura Kovacs},
  series    = {EPiC Series in Computing},
  volume    = {73},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/VTGk},
  doi       = {10.29007/vkmj},
  pages     = {390-408},
  year      = {2020}}
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