The Complexity of Explicit Constructions

The existence of extremal combinatorial objects, such as Ramsey graphs and expanders, is often shown using the probabilistic method. It is folklore that pseudo-random generators can be used to obtain explicit constructions of these objects, if the test that the object is extremal can be implemented...

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Bibliographic Details
Published inTheory of computing systems Vol. 51; no. 3; pp. 297 - 312
Main Author Santhanam, Rahul
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.10.2012
Springer Nature B.V
Subjects
Boolean
Circuits
Combinatorial analysis
Combinatorics
Complexity
Complexity theory
Computation
Computational mathematics
Computer Science
Construction
Error correction & detection
Expanders
Folklore
Generators
Graphs
Joints
Studies
Theory of Computation
Explicit constructions
Complexity theory
Combinatorial properties
Pseudorandomness
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Summary:The existence of extremal combinatorial objects, such as Ramsey graphs and expanders, is often shown using the probabilistic method. It is folklore that pseudo-random generators can be used to obtain explicit constructions of these objects, if the test that the object is extremal can be implemented in polynomial time. In this paper, we pose several questions geared towards initiating a structural approach to the relationship between extremal combinatorics and computational complexity. One motivation for such an approach is to understand better why circuit lower bounds are hard. Another is to formalize connections between the two areas, so that progress in one leads automatically to progress in the other.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-011-9368-x