Entailment Checking in Separation Logic with Inductive Definitions is 2-EXPTIME hard

EasyChair Preprint 4877

Abstract

The entailment between separation logic formulae with inductive predicates, also known as symbolic heaps, has been shown to be decidable for a large class of inductive definitions. Recently, a 2-EXPTIME algorithm was proposed and an EXPTIME-hard bound was established; however no precise lower bound is known. In this paper, we show that deciding entailment between predicate atoms is 2-EXPTIME-hard. The proof is based on a reduction from the membership problem for exponential-space bounded alternating Turing machines.

Keyphrases: alternating Turing machines, complexity, induction, separation logic

@booklet{EasyChair:4877,
  author    = {Mnacho Echenim and Radu Iosif and Nicolas Peltier},
  title     = {Entailment Checking in Separation Logic with Inductive Definitions is 2-EXPTIME hard},
  howpublished = {EasyChair Preprint 4877},
  year      = {EasyChair, 2021}}