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A New RecursionTheoretic Characterization Of The Polytime Functions
 COMPUTATIONAL COMPLEXITY
, 1992
"... We give a recursiontheoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds. In particular, this syntactic characterization avoids the explicit size bounds on recursion (and the initial function 2 xy ) of Cobham. ..."
Abstract

Cited by 191 (7 self)
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We give a recursiontheoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds. In particular, this syntactic characterization avoids the explicit size bounds on recursion (and the initial function 2 xy ) of Cobham.
Ranking Arithmetic Proofs by Implicit Ramification
 in Proof Complexity and Feasible Arithmetics, P. Beame and S. Buss, eds., DIMACS Series in Discrete Mathematics
, 1996
"... Proofs in an arithmetic system are ranked according to a ramification hierarchy based on occurrences of induction. It is shown that this ranking of proofs corresponds exactly to a natural ranking of the primitive recursive functions based on occurrences of recursion. A function is provably convergen ..."
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Cited by 4 (3 self)
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Proofs in an arithmetic system are ranked according to a ramification hierarchy based on occurrences of induction. It is shown that this ranking of proofs corresponds exactly to a natural ranking of the primitive recursive functions based on occurrences of recursion. A function is provably convergent using a rank r proof, if and only if it is a rank r function. The result is of interest to complexity theorists, since rank one corresponds to polynomial time. Remarkably, this characterization of polynomialtime provability admits induction over formulas having arbitrary quantifier complexity. 1 Introduction The primitive recursive functions can be assigned ranks, based on an examination of the structure of their derivations as built up from the initial functions by the rules of composition and recursion. One of the hierarchies defined using such a ranking consists of the polynomialtime computable functions at level 1, and at higher levels consists of certain of the Grzegorczyk classe...