Construction
The case corresponds to pseudorandom generators for linear functions and is solved by small-bias generators. For example, the construction of Naor & Naor (1990) achieves a seed length of, which is optimal up to constant factors.
Bogdanov & Viola (2007) conjectured that the sum of small-bias generators fools low-degree polynomials and were able to prove this under the Gowers inverse conjecture. Lovett (2009) proved unconditionally that the sum of small-bias spaces fools polynomials of degree . Viola (2008) proves that, in fact, taking the sum of only small-bias generators is sufficient to fool polynomials of degree . The analysis of Viola (2008) gives a seed length of .
Read more about this topic: Pseudorandom Generators For Polynomials
Famous quotes containing the word construction:
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (18591952)
“When the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators; the instruments, not the guides, of the people.”
—Edmund Burke (17291797)
“Theres no art
To find the minds construction in the face.”
—William Shakespeare (15641616)