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Tropical Circuit Complexity: Limits of Pure Dynamic Programming (SpringerBriefs in Mathematics) book cover by Stasys Jukna
Paperback

Tropical Circuit Complexity: Limits of Pure Dynamic Programming (SpringerBriefs in Mathematics)

by Stasys Jukna

$43.99 / copy at 25+ copies As low as $42.99 at 100+Your best volume price

Total $1,099.75

Paperback · 129 pages Springer International Publishing · 2023

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About the book

Tropical Circuit Complexity

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 rigorous combinatorial nature of tropical circuits, elements from the Boolean and arithmetic circuit complexity can be used to obtain lower bounds for tropical circuits, which play a crucial role in understanding the limitations and capabilities of these computational models. This book aims to offer a toolbox for proving lower bounds on the size of tropical circuits.

In this work, the reader will find lower-bound ideas and methods that have emerged in the last few years, with detailed proofs. Largely self-contained, this book is meant to be approachable by graduate students in mathematics and computer science with a special interest in circuit complexity.


Details

Publisher
Springer International Publishing
Author
Stasys Jukna
Format
Paperback
Published
Nov 8, 2023
ISBN-13
9783031423536
Pages
129
Printing
Printed on demand
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