Pseudorandomness for read-k dnf formulas
WebJan 8, 2016 · Read-Once Formulas. A read-once formula is a circuit on \(x = (x_1,\dots ,x_n) \in \ ... otherwise we would get a non-uniform distinguisher against aggregate pseudorandomness. The case of DNF formulas (or more generally of any class for which satisfiability is tractable) was left as an important open problem in . WebSteinke, Thomas, Salil Vadhan, and Andrew Wan. “ Pseudorandomness and Fourier growth bounds for width 3 branching programs .”. Theory of Computing – Special Issue on APPROX-RANDOM 2014 13, no. 12 (2024): 1-50. Publisher's Version Abstract TOC 2024.pdf APPROX-RANDOM 2014.pdf ArXiv 2014.pdf.
Pseudorandomness for read-k dnf formulas
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WebTurning to read-kDNFs, an obvious but crucial qualitative di erence between the k= 1 (read-once) and k 2 cases is the lack of independence across terms in the latter, which … Webread‐k DNF formula (and [GKK08] gives ... 3.How we did prove it. a)Read‐once DNF formulas b)Random DNF formulas c)Read‐k DNF formulas 4.Pseudorandomness. How we didn’t prove Mansour’s Conjecture 1 Every f has a unique real polynomial representation with coeffs f(S) (the Fourier representation). Analyze the large coeffs ...
WebFor the further restricted class of read-once depth-2 circuits (i.e. CNF or DNF formulas in which every variable appears at most once), Gopalan et al. [10] constructed a … Webm 2f0;1g, are moreover a generalization of both DNF and CNF formulas. In particular, DNF formulas are the special case where b 1 = = b m 1 = 1 and b m= 0. Following custom, we count the size of a DNF formula as m 1 instead of m, and thus DL(f) DNF(f) + 1 for all Boolean functions f. Despite decision lists and DNF/CNF formulas being more complex ...
WebIn boolean logic, a disjunctive normal form ( DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept. [citation needed] As a normal form, it is useful in automated theorem proving . WebA sharp O(k 1=2) upper bound on the probability that a random binary string generated according to a k-wise independent probability measure has any given weight. An assertion …
WebPseudorandomness for read-k DNF formulas Rocco A. Servedio Li-Yang Tany Abstract The design of pseudorandom generators and deterministic approximate counting algorithms …
WebPseudorandomness e.g. PRGs and high-dimensional geometry [OST, OSTK] Learning Theory e.g. Algorithms and lower bounds for learning decision trees [ BLQT , KST ] A central … group chat transparent backgroundWebMar 11, 2024 · Lovasz Local Lemma: Statement and applications. Application 1: Satisfiablity of a k-CNF formula. Application 2: Existence of a cycle whose length is 0 modulo k. film dany boon streamingWebOur first main result is a pseudorandom generator which ε-fools M-term read-k DNFs using seed length poly(k, log(1/ε))•log M +O(log n). This seed length is exponentially shorter, as … film dance with meWebJan 2, 2024 · Our first main result is a pseudorandom generator which ε-fools M-term read-k DNFs using seed length poly(k, log(1/ε))·log M + O(log n). This seed length is … group chatting platformsWebWe use (k,t,n)-2BP to denote width 2 branching programs of length t that read k bits of input at a time and compute a function from {0,1}n to {0,1}. Our first main result is a positive one, showing that a PRG for degree k polynomials over F 2 is also a PRG for the class of functions computed by a (k,t,n)-2BP. Theorem 1.2. group chat toolsWebWe present an explicit pseudorandom generator for oblivious, read-once, width-3 branching programs, which can read their input bits in any order. The generator has seed length … film dark city 1998WebJul 15, 2024 · Pseudorandomness for read-k DNF formulas. SODA 2024: 621-638 last updated on 2024-07-15 13:49 CEST by the dblp team all metadata released as open data under CC0 1.0 license see also: Terms of Use Privacy Policy Imprint dblp was originally created in 1993 at: since 2024, dblp has been operated and maintained by: film dark city