Entailment is Undecidable for Symbolic Heap Separation Logic Formulae with Non-Established Inductive Rules

Mnacho Echenim (1) , Radu Iosif (2) , Nicolas Peltier (1)

1 LIG - Laboratoire d'Informatique de Grenoble
2 VERIMAG - IMAG - VERIMAG

Entailment is undecidable in general for Separation (SL) Logic formulae with in-ductive definitions, but it has been shown to be decidable [1] if the inductive rules satisfy three conditions, namely progress, connectivity and establishment. We show that entailment is undecidable if the latter condition is dropped, thus drawing a much clearer frontier for (un)decidability.

Mots clés: Separation Logic; Inductive Definition; Decidability

Domaines: Complexité [cs.CC]; Informatique [cs]; Architectures Matérielles [cs.AR]

Mnacho Echenim, Radu Iosif, Nicolas Peltier. Entailment is Undecidable for Symbolic Heap Separation Logic Formulae with Non-Established Inductive Rules. Information Processing Letters, 2022. ⟨hal-02951859v2⟩