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

Mnacho Echenim , Radu Iosif , Nicolas Peltier (1)

1 CAPP - Calculs algorithmes programmes et preuves

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.

Domaines: Logique en informatique [cs.LO]

Mnacho Echenim, Radu Iosif, Nicolas Peltier. Entailment Checking in Separation Logic with Inductive Definitions is 2-EXPTIME hard. LPAR 2020, 2020, Alicante, Spain. ⟨10.1145/3380809⟩. ⟨hal-02990396⟩