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Complexity Lower Bounds using Linear Algebra by Satya Lokam
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Description

While rapid progress has been made on upper bounds (algorithms), progress on lower bounds on the complexity of explicit problems has remained slow despite intense efforts over several decades. As is natural with typical impossibility results, lower bound questions are hard mathematical problems and hence are unlikely to be resolved by ad hoc attacks. Instead, techniques based on mathematical notions that capture computational complexity are necessary. Complexity Lower Bounds using Linear Algebra surveys 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. Understanding the inherent computational complexity of problems is of fundamental importance in mathematics and theoretical computer science. This is an invaluable reference for anyone working in the field.
Release date Australia
July 20th, 2009
Author
Audience
  • Professional & Vocational
Pages
176
Dimensions
156x234x10
ISBN-13
9781601982421
Product ID
3189755

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