Journal of Symbolic Logic 60 (3):952-969 (1995)

Abstract
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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Weak Second‐Order Arithmetic and Finite Automata.J. Richard Büchi - 1960 - Mathematical Logic Quarterly 6 (1-6):66-92.
Fixed-Point Extensions of First-Order Logic.Yuri Gurevich & Saharon Shelah - 1986 - Annals of Pure and Applied Logic 32:265-280.

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