The Lower Bound of Decidable Entailments in Separation Logic with Inductive Definitions

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 [4]. Recently, a 2EXPTIME algorithm has been proposed [7], however no precise lower bound is known (although a EXPTIME-hard bound for this problem has been established in [5]). In this paper, we show that deciding entailment between predicate atoms is 2EXPTIME-hard. The proof is based on a reduction from the membership problem for exponential-space bounded alternating Turing machines [3].
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Submitted on : Saturday, November 30, 2019 - 8:20:16 PM
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Mnacho Echenim, Radu Iosif, Nicolas Peltier. The Lower Bound of Decidable Entailments in Separation Logic with Inductive Definitions. 2019. ⟨hal-02388028⟩

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