EAN: 9783031423536

SPRINGERBRIEFS IN MATHEMATICS TROPICAL CIRCUI...

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.

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