Tropical Circuit Complexity: Limits of Pure Dynamic Programming

Name: Tropical Circuit Complexity: Limits of Pure Dynamic Programming
Brand: Springer
SKU: 9783031423536
Price: 3270.0 INR
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by Stasys Jukna

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ISBN13: 9783031423536
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: November 8, 2023
Pages: 129
Original Price: EUR 44.99
Language: English
Edition: 2023
Item Weight: 210 grams
BISAC Subject(s): Discrete Mathematics, Computer Science, and Applied

About The Book

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.

About The Author

Stasys Jukna is an Affiliated Researcher at Vilnius University, Lithuania. His research interests lie between mathematics and theoretical computer sciences, with a focus on proving lower bounds on circuit complexity. Dr. Jukna has authored numerous books, including "Extremal Combinatorics" and "Boolean Function Complexity," published by Springer.

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