Complexity Lower Bounds Using Linear Algebra

Download or read book Complexity Lower Bounds Using Linear Algebra written by Satyanarayana V. Lokam and published by Now Publishers Inc. This book was released on 2009-07-20 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: We survey several techniques for proving lower bounds in Boolean, algebraic, and communication complexity based on certain linear algebraic approaches. The common theme among these approaches is to study robustness measures of matrix rank that capture the complexity in a given model. Suitably strong lower bounds on such robustness functions of explicit matrices lead to important consequences in the corresponding circuit or communication models. Many of the linear algebraic problems arising from these approaches are independently interesting mathematical challenges.