Entailment Checking in Separation Logic with Inductive Definitions is 2-EXPTIME hard
Mnacho Echenim, Radu Iosif, Nicolas Peltier · EPiC series in computing · 2020
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].