Explicit constructions of extractors and expanders
نویسندگان
چکیده
منابع مشابه
Recent Developments in Explicit Constructions of Extractors
Extractors are functions which are able to “extract” random bits from arbitrary distributions which “contain” sufficient randomness. Explicit constructions of extractors have many applications in complexity theory and combinatorics. This manuscript is a survey of recent developments in extractors and focuses on explicit constructions of extractors following Trevisan’s breakthrough result [Tre99].
متن کاملMonotone Expanders: Constructions and Applications
The main purpose of this work is to formally define monotone expanders and motivate their study with (known and new) connections to other graphs and to several computational and pseudorandomness problems. In particular we explain how monotone expanders of constant degree lead to: 1. constant-degree dimension expanders in finite fields, resolving a question of Barak, Impagliazzo, Shpilka, and Wi...
متن کاملRandomness extractors -- applications and constructions
Randomness extractors are efficient algorithms which convert weak random sources into nearly perfect ones. While such purification of randomness was the original motivation for constructing extractors, these constructions turn out to have strong pseudorandom properties which found applications in diverse areas of computer science and combinatorics. We will highlight some of the applications, as...
متن کاملLecture 9 : Expanders Part 2 , Extractors
In the previous lecture we saw the definitions of eigenvalue expanders, edge expanders, and vertex expanders for d-regular graphs. To recap, in an eigenvalue expander, all except the first eigenvalue of the graph’s adjacency matrix are bounded below d. In an edge expander, every subset of vertices of size below a certain threshold has a large number of edges “going out” of the subset. And in a ...
متن کاملExplicit Unique-Neighbor Expanders
We present a simple, explicit construction of an infinite family F of bounded-degree ’unique-neighbor’ expanders Γ; i.e., there are strictly positive constants α and , such that all Γ = (X,E(Γ)) ∈ F satisfy the following property. For each subset S of X with no more than α|X| vertices, there are at least |S| vertices in X \ S that are adjacent in Γ to exactly one vertex in S. The construction o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2009
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa140-3-2