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Tailoring recursion for complexity

Published online by Cambridge University Press:  12 March 2014

Erich Grädel  and
Yuri Gurevich
Erich Grädel
Affiliation:
Lehrgebiet Math. Grundlagen der Informatik, RWTH Aachen, D-52056 Aachen, Germany, E-mail: graedel@informatik.rwth-aachen.de
Yuri Gurevich
Affiliation:
EECS Department, University of Michigan, Ann Arbor, MI 48109-2122, USA, E-mail: gurevich@umich.edu
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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 AC1 -circuits.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 3 , September 1995 , pp. 952 - 969
Copyright
Copyright © Association for Symbolic Logic 1995

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