منابع مشابه
Algorithmic polynomials
The approximate degree of a Boolean function f(x1, x2, . . . , xn) is the minimum degree of a real polynomial that approximates f pointwise within 1/3. Upper bounds on approximate degree have a variety of applications in learning theory, differential privacy, and algorithm design in general. Nearly all known upper bounds on approximate degree arise in an existential manner from bounds on quantu...
متن کاملAlgorithmic regularity for polynomials and applications
In analogy with the regularity lemma of Szemerédi [Sze75], regularity lemmas for polynomials shown by Green and Tao [GT09] and by Kaufman and Lovett [KL08] give a way of modifying a given collection of polynomials F = {P1, . . . , Pm} to a new collection F ′ so that the polynomials in F ′ are “pseudorandom”. These lemmas have various applications, such as (special cases) of Reed-Muller testing ...
متن کاملAlgorithmic Work with Orthogonal Polynomials and Special Functions
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types of identities for those functions. Some of these identities like differential equations, power series representations, and hypergeometric representations can ...
متن کاملAlgorithmic aspects of sums of Hermitian squares of noncommutative polynomials
This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of the classical Gram matrix method and the Newton polytope method, which allows us to use semidefinite programming. Throughout the paper several...
متن کاملParallel Genetic Algorithm Using Algorithmic Skeleton
Algorithmic skeleton has received attention as an efficient method of parallel programming in recent years. Using the method, the programmer can implement parallel programs easily. In this study, a set of efficient algorithmic skeletons is introduced for use in implementing parallel genetic algorithm (PGA).A performance modelis derived for each skeleton that makes the comparison of skeletons po...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2020
ISSN: 0097-5397,1095-7111
DOI: 10.1137/19m1278831