Beyond Symbolic Heaps: Deciding Separation Logic With Inductive Definitions

19 pages•Published: 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.

Links:	https://easychair.org/publications/paper/VTGk
	https://doi.org/10.29007/vkmj