Stasys Jukna: Tropical Circuit Complexity

Cover: 9783031423536 | Tropical Circuit Complexity | Limits of Pure Dynamic Programming | ix

Rückseite: 9783031423536 | Tropical Circuit Complexity | Limits of Pure Dynamic Programming | ix

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

Presents tropical circuits and their use in combinatorial, discrete optimization problems

Offers a toolbox for proving lower bounds for tropical circuits, facilitating the study of their complexity

Gathers ideas and methods that have, until now, been scattered throughout the literature

Inhaltsverzeichnis

Chapter. 1. Basics.- Chapter. 2. Combinatorial Bounds.- Chapter. 3. Rectangle Bounds.- Chapter. 4. Bounds for Approximating Circuits.- Chapter. 5. Tropical Branching Programs.- Chapter. 6. Extended Tropical Circuits.

Erscheinungsjahr:	2023
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	ix 129 S. 19 s/w Illustr. 129 p. 19 illus.
ISBN-13:	9783031423536
ISBN-10:	3031423534
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Jukna, Stasys
Auflage:	1st edition 2023
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 8 mm
Von/Mit:	Stasys Jukna
Erscheinungsdatum:	08.11.2023
Gewicht:	0,224 kg

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