Tailoring recursion for complexity

Journal of Symbolic Logic 60 (3):952-969 (1995)
We design functional algebras that characterize various complexity classes of global functions. For this purpose, classical schemata from recursion theory are tailored for capturing complexity. In particular we present a functional analog of first-order logic and describe algebras of the functions computable in nondeterministic logarithmic space, deterministic and nondeterministic polynomial time, and for the functions computable by AC 1 -circuits
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DOI 10.2307/2275767
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J. Richard Büchi (1960). Weak Second-Order Arithmetic and Finite Automata. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 6 (1-6):66-92.

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