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Notes on Polynomially Bounded Arithmetic
"... We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general modeltheoretical investigations on fragments of bounded arithmetic. Contents 0 Introduction and motivation. 1 1 Preliminaries. 3 1.1 The p ..."
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Cited by 58 (1 self)
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We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general modeltheoretical investigations on fragments of bounded arithmetic. Contents 0 Introduction and motivation. 1 1 Preliminaries. 3 1
ON POLYNOMIALLY BOUNDED WEIGHTED SHIFTS
"... L(H) the algebra of bounded linear operators on H. An operator T in L(H) is said to be polynomially bounded (notation: T ∈ (PB)) if there exists an M> 0 such that (1) ‖p(T) ‖ ≤M sup{p(ζ)  : ζ  = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial ..."
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Cited by 2 (1 self)
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L(H) the algebra of bounded linear operators on H. An operator T in L(H) is said to be polynomially bounded (notation: T ∈ (PB)) if there exists an M> 0 such that (1) ‖p(T) ‖ ≤M sup{p(ζ)  : ζ  = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every
Polynomially bounded matrix interpretations
 In Proc. 21st RTA, volume 6 of LIPIcs
, 2010
"... Abstract. Matrix interpretations can be used to bound the derivational complexity of rewrite systems. We present a criterion that completely characterizes matrix interpretations that are polynomially bounded. It includes the method of upper triangular interpretations as a special case, and we prove ..."
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Cited by 9 (0 self)
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Abstract. Matrix interpretations can be used to bound the derivational complexity of rewrite systems. We present a criterion that completely characterizes matrix interpretations that are polynomially bounded. It includes the method of upper triangular interpretations as a special case, and we prove
LOCALLY POLYNOMIALLY BOUNDED STRUCTURES
, 2007
"... We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally definable in a fixed ominimal and polynomially bounded reduct. As ..."
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Cited by 7 (4 self)
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We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally definable in a fixed ominimal and polynomially bounded reduct
POLYNOMIAL BOUNDS FOR RINGS OF INVARIANTS
, 2000
"... Hilbert proved that invariant rings are finitely generated for linearly reductive groups acting rationally on a finite dimensional vector space. Popov gave an explicit upper bound for the smallest integer d such that the invariants of degree ≤ d generate the invariant ring. This bound has factorial ..."
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Cited by 11 (2 self)
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factorial growth. In this paper we will give a bound which depends only polynomially on the input data.
On boosting with polynomially bounded distributions
 Journal of Machine Learning Research
"... Abstract We construct a framework which allows an algorithm to turn the distributions produced by some boosting algorithms into polynomially smooth distributions (w.r.t. the PAC oracle's distribution), with minimal performance loss. Further, we explore the case of Freund and Schapire's Ad ..."
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Cited by 6 (0 self)
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's AdaBoost algorithm, bounding its distributions to polynomially smooth. The main advantage of AdaBoost over other boosting techniques is that it is adaptive, i.e., it is able to take advantage of weak hypotheses that are more accurate than it was assumed a priori. We show that the feature
On the diameter of the symmetric group: polynomial bounds
 In: Proceedings of the Fifteenth Annual ACMSIAM Symposium on Discrete Algorithms
"... Abstract We address the longstanding conjecture that all permutations have polynomially bounded word length in terms of any set of generators of the symmetric group. The best available bound on the maximum required word length is exponential in √ n log n. Polynomial bounds on the word length have ..."
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Cited by 13 (5 self)
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Abstract We address the longstanding conjecture that all permutations have polynomially bounded word length in terms of any set of generators of the symmetric group. The best available bound on the maximum required word length is exponential in √ n log n. Polynomial bounds on the word length have
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