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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.
Cited literature [20 references]
https://hal.archives-ouvertes.fr/hal-02323468
Contributor : Nicolas Peltier Connect in order to contact the contributor
Submitted on : Tuesday, November 5, 2019 - 10:06:47 AM
Last modification on : Wednesday, November 3, 2021 - 6:45:52 AM
Long-term archiving on: : Thursday, February 6, 2020 - 11:03:26 PM
Contributor : Nicolas Peltier Connect in order to contact the contributor
Submitted on : Tuesday, November 5, 2019 - 10:06:47 AM
Last modification on : Wednesday, November 3, 2021 - 6:45:52 AM
Long-term archiving on: : Thursday, February 6, 2020 - 11:03:26 PM
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