Complexity Lower Bounds using Linear Algebra (Foundations by Satyanarayana V. Lokam PDF

By Satyanarayana V. Lokam

Show description

Read or Download Complexity Lower Bounds using Linear Algebra (Foundations and Trends in Theoretical Computer Science) PDF

Best computers books

New PDF release: Bayesian Approach to Image Interpretation

Writing for college kids and researchers within the box, Kopparapu (research and improvement for a personal corporation in Bangalore, India) and Desai (electrical engineering, Indian Institute of know-how, Bombay) current an outline and up to date therapy of photo interpretation. The preliminary chapters describe the kingdom of study, Markov random fields, their program to desktop imaginative and prescient, the idea that of cliques, and Bayesian community photo interpretation.

Arjan Kuijper (auth.), Lewis D. Griffin, Martin Lillholm's Scale Space Methods in Computer Vision: 4th International PDF

This ebook constitutes the refereed court cases of the 4th foreign convention on Scale area tools in desktop imaginative and prescient, Scale-Space 2003, held at Isle of Skye, united kingdom in June 2003. The fifty six revised complete papers offered have been conscientiously reviewed and chosen from one zero one submissions. The booklet bargains topical sections on deep constitution representations, scale area arithmetic, equivalences, imposing scale areas, minimum methods, evolution equations, neighborhood constitution, photograph types, morphological scale areas, temporal scale areas, form, and movement and stereo.

Sustainable Enterprise: Profiting from Best Practice by Christopher Stephen Brown PDF

Instructed via the Institute of administrators a pragmatic advisor to the strategic and working demanding situations in turning into a sustainable firm Perceptions of a business's sustainability may have a true effect at the bottom-line. The rewards for accountability, responsibility and transparency should be excessive: model loyalty, high-caliber recruits, bolstered partnerships, more uncomplicated access to new markets and higher entry to capital.

Download e-book for iPad: Computers and Education in the 21st Century by Manuel Ortega, José Bravo

This cutting-edge quantity includes chosen papers at the newest study within the implementation of desktops in schooling. The subject matters coated diversity from web-based functions to interactive platforms for studying. The booklet should be of significant curiosity to lecturers, academics, researchers, complex scholars, and alertness designers on pcs in schooling in addition to managers of academic associations.

Extra info for Complexity Lower Bounds using Linear Algebra (Foundations and Trends in Theoretical Computer Science)

Sample text

We thus get a 2r × (n − 2rR/n) submatrix B that contains no changes and hence is a submatrix of H. By definition of R, this submatrix must have rank at most r. 6, we get r ≥ rank(B) ≥ 2r(n − 2rR/n)/n, since B 2F is exactly the number entries in B. Rearranging this inequality, we get R ≥ n2 /4r. 1. Kashin and Razborov [42] also use spectral methods to prove an Ω(n2 /r) lower bound on the rigidity of a generalized Hadamard matrix. The essential claim in their paper is that a random k × k submatrix of a generalized Hadamard matrix has rank Ω(k).

4) and [83]. Morgenstern used determinantal arguments to prove an Ω(n log n) lower bound on the bounded coefficient complexity of the Fourier transform. We will give a more general proof of the statement based on [83]. We will also give a proof due to Pudl´ ak which also uses bounds on the determinant, but in a different way from Morgenstern. His proof has the nice feature that it gives the strongest bounds known to date on constant depth circuits as well. The main lemma for his result is the following.

The proof of Morgenstern, discussed later, however, gives a much better lower bound of log det(A)/ log 2c with no assumptions on the depth. Proof. A depth-d synchronous circuit can be viewed as consisting of d layers of intermediate nodes with i nodes on level i (inputs at level 0, outputs at level d). The edges from level i to level i + 1 define an i × i+1 matrix Ai+1 , where 0 = d = n. We thus have A = A1 · · · Ad . 14 to this factorization of A. Now, note that if si is the number of edges from level i − 1 to level i, then, Ai 2F ≤ si c2 .

Download PDF sample

Complexity Lower Bounds using Linear Algebra (Foundations and Trends in Theoretical Computer Science) by Satyanarayana V. Lokam

by James

Rated 4.19 of 5 – based on 36 votes