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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 analogue 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. 1 Introduction The design and... (Update)
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BibTeX entry: (Update)
@misc{ del-tailoring,
author = "Erich Grädel and Yuri Gurevich",
title = "Tailoring Recursion for Complexity",
url = "citeseer.ist.psu.edu/21087.html" }
Citations (may not include all citations):379 Complexity of Relational Query Languages (context) - Vardi - 1982
245 Relational queries computable in polynomial time - Immerman - 1986
211 Languages that Capture Complexity Classes - Immerman - 1987
210 Generalized first-order spectra and polynomial-time recogniz.. (context) - Fagin - 1974
170 Nondeterministic space is closed under complementation - Immerman - 1988
149 Logic and the Challenge of Computer Science (context) - Gurevich - 1988
124 Datalog Extensions for Database Queries and Updates (context) - Abiteboul, Vianu - 1991
103 Bounded Arithmetic (context) - Buss - 1986
100 Weak second-order arithmetic and finite automata (context) - Buchi - 1960
96 A New Recursion-Theoretic Characterization of the Polytime F.. (context) - Bellantoni, Cook - 1992
95 Fixed Point Extensions of First Order Logic (context) - Gurevich, Shelah - 1986
85 Upper and lower bounds for first-order expressibility (context) - Immerman - 1982
61 Descriptive and Computational Complexity - Immerman - 1989
42 The Method of Forced Enumeration for Nondeterministic Automa.. (context) - Szelepcs'enyi - 1988
39 Algebras of feasible functions (context) - Gurevich - 1983
38 The intrinsic computational difficulty of functions (context) - Cobham - 1965
26 Inductive Definability with Counting on Finite Structures - Gradel, Otto - 1993
19 Polynomial computability and recursivity in finite domains (context) - Sazonov - 1980
15 Finite automata and the logic of monadic predicates (context) - Trakhtenbrot - 1961
10 Capturing Complexity Classes by Fragments of Second Order Lo.. (context) - Gradel - 1992
10 A Logic for Constant-Depth Circuits (context) - Gurevich, Lewis - 1984
6 Characterizing complexity classes by general recursive defin.. (context) - Goerdt - 1989
5 Automatic Documentation and Mathematical Linguistics (context) - Livchak, Model et al. - 1983
4 Information and Computation (context) - Compton, Laflamme et al. - 1990
3 Toward logic tailord for computational complexity (context) - Gurevich - 1984
1 Functions and Functionals on Finite Systems (context) - Lo - 1992
1 The Complexity of Optimizaton Problems (context) - Krentel - 1988
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