Abstract
We define a theory of two-sort bounded arithmetic whose provably total functions are exactly those in \({\mathcal{F}_{LOGCFL}}\) by way of a generalized quantifier that expresses computations of SAC 1 circuits. The proof depends on Kolokolova’s conditions for the connection between the provable capture in two-sort theories and descriptive complexity.
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Kuroda, S. Generalized quantifier and a bounded arithmetic theory for LOGCFL. Arch. Math. Logic 46, 489–516 (2007). https://doi.org/10.1007/s00153-007-0052-4
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DOI: https://doi.org/10.1007/s00153-007-0052-4