Jukna Tropical Circuit Complexity

Limits of Pure Dynamic Programming
1. Auflage 2023
ISBN: 978-3-031-42354-3
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 129 Seiten, eBook

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Jukna, Stasys

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.

Über Autor(innen)

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.