This is the first comprehensive exposition of basic lower-bounds arguments, reviewing gems discovered in the past two decades right up to results from the last year. Covers a wide spectrum of models: circuits, formulas, communication protocols, branching programs.
This is the first comprehensive exposition of basic lower-bounds arguments, reviewing gems discovered in the past two decades right up to results from...
Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this "complexity Waterloo" that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and...
Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for...
This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems.
In DP, an optimization problem is broken up into smaller subproblems that are solved recursively. Many classical DP algorithms are pure in that they only use the basic (min,+) or (max,+) operations in their recursion equations. In tropical circuits, these operations are used as gates. Thanks to the...
This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), whi...
