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Pré-Publication, Document De Travail Année : 2018

The Complexity of Prenex Separation Logic with One Selector

Mnacho Echenim
Radu Iosif
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Résumé

We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). Second, we show that this entails the decidability of the finite and infinite satisfiability problem for the class of prenex formulas of $\seplogk{1}$, by reduction to the first-order theory of one unary function symbol and unary predicate symbols. We also prove that the complexity is not elementary, by reduction from the first-order theory of one unary function symbol. Finally, we prove that the Bernays-Sch\"onfinkel-Ramsey fragment of prenex $\seplogk{1}$ formulae with quantifier prefix in the language $\exists^*\forall^*$ is \pspace-complete. The definition of a complete (hierarchical) classification of the complexity of prenex $\seplogk{1}$, according to the quantifier alternation depth is left as an open problem.

Dates et versions

hal-01946528 , version 1 (06-12-2018)

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Mnacho Echenim, Radu Iosif, Nicolas Peltier. The Complexity of Prenex Separation Logic with One Selector. 2018. ⟨hal-01946528⟩
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