Towards Optimal Randomness Extractors and Ramsey Graphs
نویسنده
چکیده
I will survey some of the recent exciting progress on explicit constructions of randomness extractors for independent sources. Many of the new constructions rely on explicit constructions of newly introduced pseudorandom primitives, and there remains scope of finding better explicit constructions of these primitives. I will also discuss some possible approaches for constructing optimal Ramsey graphs and Extractors. Faculty Host: Rutgers/DIMACS Theory of Computing
منابع مشابه
Pseudorandom Correlation Breakers, Independence Preserving Mergers and their Applications
The recent line of study on randomness extractors has been a great success, resulting in exciting new techniques, new connections, and breakthroughs to long standing open problems in the following five seemingly different topics: seeded non-malleable extractors, privacy amplification protocols with an active adversary, independent source extractors (and explicit Ramsey graphs), non-malleable in...
متن کاملAn E icient Reduction from Two-Source to Non-malleable Extractors
The breakthrough result of Chattopadhyay and Zuckerman (2016) gives a reduction from the construction of explicit two-source extractors to the construction of explicit non-malleable extractors. However, even assuming the existence of optimal explicit nonmalleable extractors only gives a two-source extractor (or a Ramsey graph) for poly(logn) entropy, rather than the optimal O (logn). In this pa...
متن کاملApplications of Derandomization Theory in Coding (PhD Thesis)
Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory is to eliminate or reduce the need for randomness in such randomized constructions. Towards this goal, numerous fundamental notions have been developed to p...
متن کامل2-Source Dispersers for n Entropy, and Ramsey Graphs Beating the Frankl-Wilson Construction
The main result of this paper is an explicit disperser for two independent sources on n bits, each of min-entropy k = 2 1−α0 , for some small absolute constant α0 > 0). Put differently, setting N = 2 and K = 2, we construct an explicit N ×N Boolean matrix for which no K ×K sub-matrix is monochromatic. Viewed as the adjacency matrix of a bipartite graph, this gives an explicit construction of a ...
متن کاملAll Ramsey (2K2,C4)−Minimal Graphs
Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...
متن کامل