Complexity

This is the second volume of a two volume collection on Structural Complexity. This volume assumes as a prerequisite knowledge about the topics treated in Volume I, but the present volume itself is ne

Helpful to those tasked with managing complex environments, Projects and Complexity introduces a new way of looking at projects and fostering the culture needed to achieve sustainable results. It brin

This book provides an introduction to the role of diversity in complex adaptive systems. A complex system--such as an economy or a tropical ecosystem--consists of interacting adaptive entities that pr

An ecosystem's complexity develops from the vast numbers of species interacting in ecological communities. The nature of these interactions, in turn, depends on environmental context. How do these com

An ecosystem's complexity develops from the vast numbers of species interacting in ecological communities. The nature of these interactions, in turn, depends on environmental context. How do these com

Many aspects of the internal and external workings of computers can be viewed as a series of communication processes. Communication complexity is the mathematical theory of such communication processes. It is also often used as an abstract model of other aspects of computation. This book surveys this mathematical theory, concentrating on the question of how much communication is necessary for any particular process. The first part of the book is devoted to the simple two-party model introduced by Yao in 1979, which is still the most widely studied model. The second part treats newer models developed to deal with more complicated communication processes. Finally, applications of these models, including computer networks, VLSI circuits, and data structures, are treated in the third part of the book. This is an essential resource for graduate students and researchers in theoretical computer science, circuits, networks and information theory.

This book is a state-of-the-art introduction into both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes. It presents detailed proof

This book is a state-of-the-art introduction into both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes. It presents detailed proof

This book provides a challenging and stimulating introduction to the contemporary topics of complexity and criticality, and explores their common basis of scale invariance, a central unifying theme o

This work views urban dynamics in the context of complexity theory; models and examples in scales from the local to the regional.As urban planning moves from a centralized, top-down approach to a dece

An up-to-date and critical analysis of how archaeologists study past societies, Archaeologies of Complexity addresses the nature of contemporary archaeology and the study of social change, and debates

A computer science text bridging the gap between the perceived impenetrability of computability and complexity theory and practical programming problems. Jones (computer science, U. of Copenhagen) of

This work elucidates the structure and complexity of human language in terms of the mathematics of information and computation. It strengthens Chomsky's early work on the mathematics of language, with

By considering the size of the logical network needed to perform a given computational task, the intrinsic difficulty of that task can be examined. Boolean function complexity, the combinatorial study of such networks, is a subject that started back in the 1950s and has today become one of the most challenging and vigorous areas of theoretical computer science. The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July 1990. The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium. Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase.

Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contain

Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.

"Small Dynamic Complexity Classes" was awarded the E.W. Beth Dissertation Prize 2016 for outstanding dissertations in the fields of logic, language, and information. The thesis studies the foundations

Complexity of grammatical structure has become a center of interest in recent typological and dialectological research. The contributions of the present volume discuss structural complexity from the p

Complexity theory has become popular in the natural and social sciences over the last few decades as a result of the advancements in our understanding of the complexities in natural and social phenome

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In tradit

What enables individually simple insects like ants to act with such precision and purpose as a group? How do trillions of neurons produce something as extraordinarily complex as consciousness? In this

Decision tree is a widely used form of representing algorithms and knowledge. Compact data models and fast algorithms require optimization of tree complexity. This book is a research monograph on aver

Emergence and complexity refer to the appearance of higher-level properties and behaviours of a system that obviously comes from the collective dynamics of that system's components. These properties a

Here is an accessible, algorithmically oriented guide to some of the most interesting techniques of complexity theory. The book shows that simple algorithms are at the heart of complexity theory. The

Fast track route to mastering highly complex environments Covers the fundamentals of complexity, from encouraging iconoclastic behavior and setting up formal complexity training to using scenarios an

This book explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it al

Complexity lies at the heart of social work practice and this book is designed to help students and newly-qualified social workers plan for and manage complex cases in an increasingly complex environm

Complexity lies at the heart of social work practice and this book is designed to help students and newly-qualified social workers plan for and manage complex cases in an increasingly complex environm

Complexity theory including the concepts of chaos and emergence has been considered one of the most revolutionary products of the 20th century having influence on science, technology and economics amo

This work represents the third entry of the series of works on “Chaos, Complexity and Leadership”. Contents of the book are composed from broad range of chaos, complexity and their applications in mul

Contemporary theories on complex adaptive systems stem from a natural science perspective. Paul Cilliers was one of the first complexity thinkers to translate the theoretical concepts into a qualitati

This book aims to assess the nature of morphological complexity, and the properties that distinguish it from the complexity manifested in other components of language. Of the many ways languages have

Evolution, Order and Complexity reflects topical interest in the relationship between the social and natural worlds. It represents the cutting edge of current thinking which challenges the natural/soc

Economics is changing. In the last few years it has generated a number of new approaches. One of the most promising -complexity economics - was pioneered in the 1980s and 1990s by a small team at the

The importance of complexity is well-captured by Hawking's comment: "Complexity is the science of the 21st century". From the movement of flocks of birds to the Internet, environmental sustainability,

In this book, fascinating autobiographical accounts by leading scholars in a variety of fields and disciplines provide a rich introduction to the art and science of complexity and systems thinking. We

This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.

This text covers the state of the art in multivariate algorithmics and complexity, a vital field with countless applications in modern computing. It describes the latest methods of proving parameteriz

This review volume, co-edited by Nobel laureate G Ertl, provides a broad overview on current studies in the understanding of design and control of complex chemical systems of various origins, on scale

Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. Spin Glasses a