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

04/16/2020

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by   Mnacho Echenim, et al.

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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.