Wigderson, Avi
Overview
Works:  38 works in 75 publications in 2 languages and 417 library holdings 

Roles:  Author, Editor 
Classifications:  QA267.7, 511.352 
Publication Timeline
.
Most widely held works by
Avi Wigderson
Computational complexity theory by
Steven Rudich(
Book
)
6 editions published in 2004 in English and held by 215 WorldCat member libraries worldwide
"This volume is recommended for independent study and is suitable for graduate students and researchers interested in computational complexity."Jacket
6 editions published in 2004 in English and held by 215 WorldCat member libraries worldwide
"This volume is recommended for independent study and is suitable for graduate students and researchers interested in computational complexity."Jacket
Pairwise independence and derandomization by
Michael George Luby(
Book
)
8 editions published between 1995 and 2007 in English and held by 26 WorldCat member libraries worldwide
The article is based on a series of lectures given by the authors in 1995, where the notes were scribed by the attending students. (The detailed list of scribes and other contributors can be found in the Acknowledgements section at the end of the manuscript.) The current version is essentially the same, with a few minor changes. We note that this publication takes place a decade after the lectures were given. Much has happened in the area of pseudorandomness and derandomization since, and perhaps a somewhat different viewpoint, different material, and different style would be chosen were these lectures given today. Still, the material presented is self contained, and is a prime manifestation of the "derandomization" paradigm. The material does lack references to newer work though. We recommend the reader interested in randomness, derandomization and their interplay with computational complexity to consult the following books and surveys, as well as their extensive bibliography
8 editions published between 1995 and 2007 in English and held by 26 WorldCat member libraries worldwide
The article is based on a series of lectures given by the authors in 1995, where the notes were scribed by the attending students. (The detailed list of scribes and other contributors can be found in the Acknowledgements section at the end of the manuscript.) The current version is essentially the same, with a few minor changes. We note that this publication takes place a decade after the lectures were given. Much has happened in the area of pseudorandomness and derandomization since, and perhaps a somewhat different viewpoint, different material, and different style would be chosen were these lectures given today. Still, the material presented is self contained, and is a prime manifestation of the "derandomization" paradigm. The material does lack references to newer work though. We recommend the reader interested in randomness, derandomization and their interplay with computational complexity to consult the following books and surveys, as well as their extensive bibliography
Partial derivatives in arithmetic complexity and beyond by Xi Chen(
Book
)
4 editions published in 2011 in English and held by 13 WorldCat member libraries worldwide
How complex is a given multivariate polynomial? The main point of this survey is that one can learn a great deal about the structure and complexity of polynomials by studying (some of) their partial derivatives. The bulk of the survey shows that partial derivatives provide essential ingredients in proving both upper and lower bounds for computing polynomials by a variety of natural arithmetic models. We will also see applications which go beyond computational complexity, where partial derivatives provide a wealth of structural information about polynomials (including their number of roots, reducibility and internal symmetries), and help us solve various number theoretic, geometric, and combinatorial problems
4 editions published in 2011 in English and held by 13 WorldCat member libraries worldwide
How complex is a given multivariate polynomial? The main point of this survey is that one can learn a great deal about the structure and complexity of polynomials by studying (some of) their partial derivatives. The bulk of the survey shows that partial derivatives provide essential ingredients in proving both upper and lower bounds for computing polynomials by a variety of natural arithmetic models. We will also see applications which go beyond computational complexity, where partial derivatives provide a wealth of structural information about polynomials (including their number of roots, reducibility and internal symmetries), and help us solve various number theoretic, geometric, and combinatorial problems
How to share memory in a distributed system by
Eli Upfal(
Book
)
4 editions published in 1984 in English and Undetermined and held by 8 WorldCat member libraries worldwide
We study the power of shared memory in models of parallel computation. We describe a novel distributed data structure that eliminates the need for shared memory without significantly increasing the run time of the parallel computation. More specifically we show how a complete network of processors can deterministicly simulate one PRAM step in O(log n(loglog n)2) time, when both models use n processors, and the size of the PRAM's shared memory is polynomial in n. The best previously known upper bound was the trivial O(n). We also establish that this upper bounds is nearly optimal. We prove that an online simulation of T PRAM steps by a complete network of processors requires omega(T log n) time/loglog n. A simple consequence of the upper bound is that an Ultracomputer (the only currently feasible general purpose parallel machine), can simulate one step of a PRAM (the most convenient parallel model to program), in ()((log n loglog n)2) steps
4 editions published in 1984 in English and Undetermined and held by 8 WorldCat member libraries worldwide
We study the power of shared memory in models of parallel computation. We describe a novel distributed data structure that eliminates the need for shared memory without significantly increasing the run time of the parallel computation. More specifically we show how a complete network of processors can deterministicly simulate one PRAM step in O(log n(loglog n)2) time, when both models use n processors, and the size of the PRAM's shared memory is polynomial in n. The best previously known upper bound was the trivial O(n). We also establish that this upper bounds is nearly optimal. We prove that an online simulation of T PRAM steps by a complete network of processors requires omega(T log n) time/loglog n. A simple consequence of the upper bound is that an Ultracomputer (the only currently feasible general purpose parallel machine), can simulate one step of a PRAM (the most convenient parallel model to program), in ()((log n loglog n)2) steps
On the second eigenvalue of hypergraphs by
Joel Friedman(
Book
)
2 editions published between 1989 and 1992 in English and held by 5 WorldCat member libraries worldwide
2 editions published between 1989 and 1992 in English and held by 5 WorldCat member libraries worldwide
The complexity of parallel search by
Richard M Karp(
Book
)
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
Constructing a perfect matching is in random NC by
Richard M Karp(
Book
)
2 editions published in 1985 in English and held by 5 WorldCat member libraries worldwide
This document shows that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomialbounded number of processors. It is also shown that several related problems lie in Random NC. These include: Constructing a perfect matching of maximum weight in a graph whose edge weights are given in unary notation; Constructing a maximumcardinality matching; Constructing a matching covering a set of vertices of maximum weight in a graph whose vertex weights are given in binary; and Constructing a maximum st flow in a directed graph whose edge weights are given in unary. Additional keywords: rank functions. (Author)
2 editions published in 1985 in English and held by 5 WorldCat member libraries worldwide
This document shows that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomialbounded number of processors. It is also shown that several related problems lie in Random NC. These include: Constructing a perfect matching of maximum weight in a graph whose edge weights are given in unary notation; Constructing a maximumcardinality matching; Constructing a matching covering a set of vertices of maximum weight in a graph whose vertex weights are given in binary; and Constructing a maximum st flow in a directed graph whose edge weights are given in unary. Additional keywords: rank functions. (Author)
Randomized decision tree complexity for ReadOnce Boolean functions by
Universiṭah haʻIvrit biYerushalayim(
Book
)
2 editions published between 1990 and 1992 in English and held by 4 WorldCat member libraries worldwide
Our result is a 0.51 lower bound on the exponent for every read once function. Readonce means that each input variable appears exactly once in the Boolean formula representing the function. To obtain this result we give a generalized version of a previously known lower bound for the randomized decision tree complexity of readonce functions and then combine it with restrictions arguments. This result provides a lower bound of n[superscript 0.51] on the number of positions that have to be evaluated by any randomized [alpha][beta] pruning algorithm computing the value of any 2person game tree with n final positions."
2 editions published between 1990 and 1992 in English and held by 4 WorldCat member libraries worldwide
Our result is a 0.51 lower bound on the exponent for every read once function. Readonce means that each input variable appears exactly once in the Boolean formula representing the function. To obtain this result we give a generalized version of a previously known lower bound for the randomized decision tree complexity of readonce functions and then combine it with restrictions arguments. This result provides a lower bound of n[superscript 0.51] on the number of positions that have to be evaluated by any randomized [alpha][beta] pruning algorithm computing the value of any 2person game tree with n final positions."
Monotone circuits for matching require linear depth by
Ran Raz(
Book
)
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
The complexity of graph connectivity by
Avi Wigderson(
Book
)
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Abstract: "In this paper we survey the major developments in understanding the complexity of the graph connectivity problem in several computational models, and highlight some challenging open problems."
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Abstract: "In this paper we survey the major developments in understanding the complexity of the graph connectivity problem in several computational models, and highlight some challenging open problems."
On computation with integer division by
Bettina Just(
Book
)
2 editions published in 1987 in German and English and held by 4 WorldCat member libraries worldwide
2 editions published in 1987 in German and English and held by 4 WorldCat member libraries worldwide
Composition of the universal relation by
Johan Håstad(
Book
)
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We prove that the communication complexity of the k fold composition of the universal relation on n bits is (1  o(1))kn when k= o([square root of n/log n])."
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We prove that the communication complexity of the k fold composition of the universal relation on n bits is (1  o(1))kn when k= o([square root of n/log n])."
n[Omega](log n) lower bounds on the size of depth 3 threshold circuits with AND gates at the bottom by A Razborov(
Book
)
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We present a function in ACC⁰ such that any depth 3 threshold circuit which computes this function and has AND gates at the bottom must have size n[superscript [omega](log n)]."
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We present a function in ACC⁰ such that any depth 3 threshold circuit which computes this function and has AND gates at the bottom must have size n[superscript [omega](log n)]."
Tiny families of functions with random properties : a quality size tradeoff for hashing by
Oded Goldreich(
Book
)
1 edition published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We present three explicit constructions of hash functions, which exhibit a tradeoff between the size of the family (and hence the number of random bits needed to generate a member of the family), and the quality (or error parameter) of the pseudorandom property it achieves. Unlike previous constructions, most notably universal hashing, the size of our families is essentially independent of the size of the domain on which the functions operate. The first construction is for the mixing property  mapping a proportional part of any subset of the domain to any other subset. The other two are for the extraction property  mapping any subset of the domain almost uniformly into a range smaller than it. The second and third constructions handle (respectively) the extreme situations when the range is very large or very small. We provide lower bounds showing our constructions are nearly optimal, and mention some applications of the new constructions."
1 edition published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We present three explicit constructions of hash functions, which exhibit a tradeoff between the size of the family (and hence the number of random bits needed to generate a member of the family), and the quality (or error parameter) of the pseudorandom property it achieves. Unlike previous constructions, most notably universal hashing, the size of our families is essentially independent of the size of the domain on which the functions operate. The first construction is for the mixing property  mapping a proportional part of any subset of the domain to any other subset. The other two are for the extraction property  mapping any subset of the domain almost uniformly into a range smaller than it. The second and third constructions handle (respectively) the extreme situations when the range is very large or very small. We provide lower bounds showing our constructions are nearly optimal, and mention some applications of the new constructions."
Information theoretic reasons for computational difficulty or communication complexity for circuit complexity by
Avi Wigderson(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Lower bounds on arithmetic circuits via partial derivatives : (preliminary version) by
Noam Nisan(
Book
)
3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
On readonce thershold formulae and their randomized decision tree complexity by
Universiṭah haʻIvrit biYerushalayim(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "TC⁰ is the class of functions computable by polynomialsize, constantdepth forumulae with threshold gates. ReadOnce TC⁰ (ROTC⁰) is the subclass of TC⁰ which restricts every variable to occur exactly once in the formula. Our main result is a (tight) linear lower bound on the randomized decision tree complexity of any function in ROTC⁰. This relationship between threshold circuits and decision trees bears significance on both models of computation. Regarding decision trees, this is the first class of functions for which such a strong bound is known. Regarding threshold circuits, it may be considered as a possible first step towards proving TC⁰ [is not equal to] NC¹; generalizing our lower bound to all functions in TC⁰ would establish this separation
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "TC⁰ is the class of functions computable by polynomialsize, constantdepth forumulae with threshold gates. ReadOnce TC⁰ (ROTC⁰) is the subclass of TC⁰ which restricts every variable to occur exactly once in the formula. Our main result is a (tight) linear lower bound on the randomized decision tree complexity of any function in ROTC⁰. This relationship between threshold circuits and decision trees bears significance on both models of computation. Regarding decision trees, this is the first class of functions for which such a strong bound is known. Regarding threshold circuits, it may be considered as a possible first step towards proving TC⁰ [is not equal to] NC¹; generalizing our lower bound to all functions in TC⁰ would establish this separation
Deterministic simulation of probabilistic constant depth circuits by
Thomas J. Watson IBM Research Center(
Book
)
3 editions published between 1985 and 1986 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 1985 and 1986 in English and held by 3 WorldCat member libraries worldwide
Oneway functions are essential for nontrivial zeroknowledge by
Rafail Ostrovsky(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Abstract: "It was known that if oneway functions exist, then there are zeroknowledge proofs for every language in PSPACE. We prove that unless very weak oneway functions exist, ZeroKnowledge proofs can be given only for languages in BPP. For averagecase definitions of BPP we prove an analagous result under the assumption that uniform oneway functions do not exist. Thus, very loosely speaking, zeroknowledge is either useless (exists only for 'easy' languages), or universal (exists for every provable language)."
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Abstract: "It was known that if oneway functions exist, then there are zeroknowledge proofs for every language in PSPACE. We prove that unless very weak oneway functions exist, ZeroKnowledge proofs can be given only for languages in BPP. For averagecase definitions of BPP we prove an analagous result under the assumption that uniform oneway functions do not exist. Thus, very loosely speaking, zeroknowledge is either useless (exists only for 'easy' languages), or universal (exists for every provable language)."
Pairwise independence and derandomization by
Michael George Luby(
)
1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide
The article is based on a series of lectures given by the authors in 1995, where the notes were scribed by the attending students. (The detailed list of scribes and other contributors can be found in the Acknowledgements section at the end of the manuscript.) The current version is essentially the same, with a few minor changes. We note that this publication takes place a decade after the lectures were given. Much has happened in the area of pseudorandomness and derandomization since, and perhaps a somewhat different viewpoint, different material, and different style would be chosen were these lectures given today. Still, the material presented is self contained, and is a prime manifestation of the "derandomization" paradigm. The material does lack references to newer work though. We recommend the reader interested in randomness, derandomization and their interplay with computational complexity to consult the following books and surveys, as well as their extensive bibliography
1 edition published in 2006 in English and held by 0 WorldCat member libraries worldwide
The article is based on a series of lectures given by the authors in 1995, where the notes were scribed by the attending students. (The detailed list of scribes and other contributors can be found in the Acknowledgements section at the end of the manuscript.) The current version is essentially the same, with a few minor changes. We note that this publication takes place a decade after the lectures were given. Much has happened in the area of pseudorandomness and derandomization since, and perhaps a somewhat different viewpoint, different material, and different style would be chosen were these lectures given today. Still, the material presented is self contained, and is a prime manifestation of the "derandomization" paradigm. The material does lack references to newer work though. We recommend the reader interested in randomness, derandomization and their interplay with computational complexity to consult the following books and surveys, as well as their extensive bibliography
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Related Identities
 Rudich, Steven Author Editor
 Luby, Michael George Author
 Chen, Xi Author
 Kayal, Neeraj
 Upfal, Eli Author
 Karp, Richard M. 1935 Author
 Heiman, Rafi Author
 Goldreich, Oded Author
 Meyer auf der Heide, Friedhelm Author
 Nisan, Noam Author
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Associated Subjects
Algorithms Computational complexity Computer scienceMathematics Computer scienceStatistical methods Cryptography Differential equations, Partial Eigenvalues Graph theoryData processing Hashing (Computer science) Matching theoryData processing Monotone operators Numbers, Random Parallel processing (Electronic computers) Polynomials Random number generatorsComputer programs Search theory Set theory
Alternative Names
Avi Wigderson
Avi Wigderson Israeli mathematician and computer scientist
Avi Wigderson israelischer Mathematiker und Informatiker
Avi Wigderson matemático, profesor e informático teórico israelí
Avi Wigderson wiskundige uit Israël
Вигдерсон, Ави
آوی ویگدرسون ریاضیدان و دانشمند علوم کامپیوتر اسرائیلی
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