Prenex Separation Logic with One Selector Field

Abstract : We show that infinite satisfiability can be reduced to finite satisfiabil-ity for all prenex formulas of Separation Logic with k ≥ 1 selector fields (SL k). This fact entails the decidability of the finite and infinite satisfiability problems for the class of prenex formulas of SL 1 , by reduction to the first-order theory of a single unary function symbol and an arbitrary number of unary predicate symbols. We also prove that the complexity of this fragment is not elementary recursive, by reduction from the first-order theory of one unary function symbol. Finally, we prove that the Bernays-Schönfinkel-Ramsey fragment of prenex SL 1 formulas with quantifier prefix in the language ∃ * ∀ * is PSPACE-complete.
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Submitted on : Tuesday, November 5, 2019 - 10:06:47 AM
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Mnacho Echenim, Radu Iosif, Nicolas Peltier. Prenex Separation Logic with One Selector Field. Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, 2019, London, United Kingdom. pp.409-427, ⟨10.1007/978-3-030-29026-9_23⟩. ⟨hal-02323468⟩

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