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

21 pages•Published: May 27, 2020

Mnacho Echenim, Radu Iosif and Nicolas Peltier

Abstract

The entailment between separation logic formulæ with inductive predicates, also known as sym- bolic heaps, has been shown to be decidable for a large class of inductive definitions [7]. Recently, a 2-EXPTIME algorithm was proposed [10, 14] and an EXPTIME-hard bound was established in [8]; 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 [5].

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

In: Elvira Albert and Laura Kovacs (editors). LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 73, pages 191-211.

Links:	https://easychair.org/publications/paper/DdNg
	https://doi.org/10.29007/f5wh

BibTeX entry

@inproceedings{LPAR23:Entailment_Checking_Separation_Logic,
  author    = {Mnacho Echenim and Radu Iosif and Nicolas Peltier},
  title     = {Entailment Checking in Separation Logic with Inductive Definitions is 2-EXPTIME hard},
  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/DdNg},
  doi       = {10.29007/f5wh},
  pages     = {191-211},
  year      = {2020}}

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