Elements of The Theory of Computation

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.

This book describes reversible computing from the standpoint of the theory of automata and computing. It investigates how reversibility can be effectively utilized in computing. A reversible computing system is a “backward deterministic” system such that every state of the system has at most one predecessor. Although its definition is very simple, it is closely related to physical reversibility, one of the fundamental microscopic laws of Nature. Authored by the leading scientist on the subject, this book serves as a valuable reference work for anyone working in reversible computation or in automata theory in general.

Clearly, nature has been very effective in creating organisms that are capable of protecting themselves against a wide variety of pathogens such as bacteria, fungi, and parasites. The powerful information-processing capabilities of the immune system, such as feature extraction, pattern recognition, learning, memory, and its distributive nature provide rich metaphors that researchers are finding very useful for the development of computational models.

Authors: Morfonios, Christian, Schmelcher, Peter
Gives formulas for computational quantum transport in multiterminal and multiply connected structures
Explains magnetoconductance switching in the deep quantum regime
Discusses directional transport in nanostructures

In this book the coherent quantum transport of electrons through two-dimensional mesoscopic structures is explored in dependence of the interplay between the confining geometry and the impact of applied magnetic fields, aiming at conductance controllability.