Titlebook: Deterministic Extraction from Weak Random Sources; Ariel Gabizon Book 2011 Springer-Verlag Berlin Heidelberg 2011 Affine sources.Derandomi

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Peng-Fei Peng,Yi-Jui Chiu,Xiao-Yun Liinite fields. This naturally generalizes previous work on extraction from affine sources (which are degree 1 polynomials). A direct consequence is a deterministic extractor for distributions sampled by polynomial-size arithmetic circuits over exponentially large fields..The steps in our extractor co

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https://doi.org/10.1007/978-3-642-14903-0Affine sources; Derandomization; Deterministic extractors; Dispersers; Randomness extractors; Recycling r

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978-3-642-26538-9Springer-Verlag Berlin Heidelberg 2011

Breach

https://doi.org/10.1007/978-981-15-3308-2An .-. over a finite field . is a random variable ., which is uniformly distributed over an (unknown) .-dimensional affine subspace of .. We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger than . (where . is a large enough constant). This chapter is based on [25].

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Deterministic Extractors for Affine Sources over Large Fields,An .-. over a finite field . is a random variable ., which is uniformly distributed over an (unknown) .-dimensional affine subspace of .. We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger than . (where . is a large enough constant). This chapter is based on [25].

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Introduction,to extractors and a sketch of the techniques and results of this work. We begin in Section 1.2 with what may be called the ‘classical motivation’ for extractors. Section 1.3 describes other motivations for deterministic extractors. In Section 1.4 we describe some of the main techniques used in this

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Book 2011tructs deterministic extractors for several types of sources. A basic theme in this work is a methodology of recycling randomness which enables increasing the output length of deterministic extractors to near optimal length.The author‘s main work examines deterministic extractors for bit-fixing sour