Tropical Circuit Complexity: Limits of Pure Dynamic Programming

· Springer Nature
E-boek
129
Bladsye

Meer oor hierdie e-boek

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.

Meer oor die skrywer

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.

Gradeer hierdie e-boek

Sê vir ons wat jy dink.

Lees inligting

Slimfone en tablette
Installeer die Google Play Boeke-program vir Android en iPad/iPhone. Dit sinkroniseer outomaties met jou rekening en maak dit vir jou moontlik om aanlyn of vanlyn te lees waar jy ook al is.
Skootrekenaars en rekenaars
Jy kan jou rekenaar se webblaaier gebruik om na oudioboeke wat jy op Google Play gekoop het, te luister.
E-lesers en ander toestelle
Om op e-inktoestelle soos Kobo-e-lesers te lees, moet jy ’n lêer aflaai en dit na jou toestel toe oordra. Volg die gedetailleerde hulpsentrumaanwysings om die lêers na ondersteunde e-lesers toe oor te dra.