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On the RandomSelfReducibility . . .
 SIAM JOURNAL ON COMPUTING
, 1993
"... In this paper, we generalize the previous formal definitions of randomselfreducibility. We show that, even under our very general definition, sets that are complete for any level of the polynomial hierarchy are not nonadaptively randomselfreducible, unless the hierarchy collapses. In particular ..."
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In this paper, we generalize the previous formal definitions of randomselfreducibility. We show that, even under our very general definition, sets that are complete for any level of the polynomial hierarchy are not nonadaptively randomselfreducible, unless the hierarchy collapses
RandomSelfReducibility
, 2004
"... We consider ArthurMerlin proof systems where (a) Arthur is a probabilistic quasipolynomial time Turing machine, denoted AMqpoly, and (b) Arthur is a probabilistic exponential time Turing machine, denoted AMexp. We prove two new results related to these classes. We show that if coNP is in AMqpoly ..."
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NP is in AMqpoly then the exponential hierarchy collapses to AMexp. We show that if SAT is polylogarithmic round adaptive randomselfreducible, then SAT is in AMqpoly with a polynomial advice. The first result improves a recent result of Selman and Sengupta (2004) who showed that the hypothesis collapses
RandomSelfReducibility In The Polynomial Hierarchy
"... In this paper, we define the concept of randomselfreducibility and provide intuitive motivation for the definition. We then introduce the concept of polynomial advice, and use it to prove the central result due to Feigenbaum and Fortnow: If some NPcomplete language is randomselfreducible, then ..."
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In this paper, we define the concept of randomselfreducibility and provide intuitive motivation for the definition. We then introduce the concept of polynomial advice, and use it to prove the central result due to Feigenbaum and Fortnow: If some NPcomplete language is randomselfreducible
On Coherence, RandomSelfReducibility, and SelfCorrection
 In Proc. 11th Conference on Computational Complexity
, 1997
"... . We study three types of selfreducibility that are motivated by the theory of program verification. A set A is randomselfreducible if one can determine whether an input x is in A by making random queries to an Aoracle. The distribution of each query may depend only on the length of x. A set B i ..."
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Cited by 11 (6 self)
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. We study three types of selfreducibility that are motivated by the theory of program verification. A set A is randomselfreducible if one can determine whether an input x is in A by making random queries to an Aoracle. The distribution of each query may depend only on the length of x. A set B
Stronger Separations for RandomSelfReducibility, Rounds, and Advice
 In IEEE Conference on Computational Complexity
, 1999
"... A function f is selfreducible if it can be computed given an oracle for f . In a randomselfreduction the queries must be made in such a way that the distribution of the ith query is independent of the input that gave rise to it. Randomself reductions have many applications, including countless c ..."
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Cited by 4 (2 self)
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is randomselfreducible with 2 rounds of queries, but which is not even coherent, even if polynomial advice is allowed, when the queries must be made in a single round. 1 Introduction Informally, we say that a function f selfreduces if it can be computed efficiently by making queries to f . For a
An InformationTheoretic Treatment of RandomSelfReducibility
 Proc. of the 14'th Symposium on Theoretical Aspects of Computer Science
, 1997
"... We initiate the study of randomselfreducibility from an informationtheoretic point of view. Specifically, we formally define the notion of a randomselfreduction that, with respect to a given ensemble of distributions, leaks a limited number bits, i.e., produces target instances y1 ; : : : ; yk ..."
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Cited by 1 (1 self)
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We initiate the study of randomselfreducibility from an informationtheoretic point of view. Specifically, we formally define the notion of a randomselfreduction that, with respect to a given ensemble of distributions, leaks a limited number bits, i.e., produces target instances y1 ; : : : ; yk
Lower Bounds on RandomSelfReducibility (Extended Abstract)
, 1990
"... Structures1990 Proceedings) Joan Feigenbaum Sampath Kannan y Noam Nisan z Abstract: Informally speaking, a function f is randomselfreducible if, for any x, the computation of f(x) can be reduced to the computation of f on other "randomly chosen" inputs. Such functions are fundam ..."
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Structures1990 Proceedings) Joan Feigenbaum Sampath Kannan y Noam Nisan z Abstract: Informally speaking, a function f is randomselfreducible if, for any x, the computation of f(x) can be reduced to the computation of f on other "randomly chosen" inputs. Such functions
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 539 (20 self)
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This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 860 (27 self)
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We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can
Results 1  10
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