Schemata of Formulæ in the Theory of Arrays

Nicolas Peltier (1)

1 LIG - Laboratoire d'Informatique de Grenoble

We consider schemata of quantifier-free formulæ, defined using indexed symbols and iterated connectives ranging over intervals (such as ⋁ni=1ϕ or ⋀ni=1ϕ ), and interpreted in the theory of arrays (with the usual functions for storing and selecting elements in an array). We first prove that the satisfiability problem is undecidable (it is clearly semi-decidable). We then consider a natural restriction on the considered structures and we prove that it makes the logic decidable by providing a sound, complete and terminating proof procedure.

Domaines: Logique en informatique [cs.LO]

Nicolas Peltier. Schemata of Formulæ in the Theory of Arrays. TABLEAUX 2013 - 22th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Sep 2013, Nancy, France. pp.234-249, ⟨10.1007/978-3-642-40537-2_20⟩. ⟨hal-00934604⟩