Simplistic Complexity

'History makes plain the complexity and contingency of human affairs and the range and variety of human experience; it enjoins suspicion of simplistic analysis, simplistic explanation, and simplistic

"Beyond previous more simplistic approaches, this book takes a giant step towards understanding and translating into people-centered policies the actual position and complexity of fish production in S

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

Computational Complexity of Counting and Sampling provides readers with comprehensive and detailed coverage of the subject of computational complexity. It is primarily geared for researchers in enumer

Computational Complexity of Counting and Sampling provides readers with comprehensive and detailed coverage of the subject of computational complexity. It is primarily geared for researchers in enumer

Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decid

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.

The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and proc

This book discusses computational complexity of High Efficiency Video Coding (HEVC) encoders with coverage extending from the analysis of HEVC compression efficiency and computational complexity to th

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

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

This book examines the question of whether languages can differ in grammatical complexity and, if so, how relative complexity differences might be measured. The volume differs from others devoted to t

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,

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

Praise for the First Edition "...complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity." -Zentralblatt MATH

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.

There is a widespread assumption that the universe in general, and life in particular, is 'getting more complex with time'. This book brings together a wide range of experts in science, philosophy and theology and unveils their joint effort in exploring this idea. They confront essential problems behind the theory of complexity and the role of life within it: what is complexity? When does it increase, and why? Is the universe evolving towards states of ever greater complexity and diversity? If so, what is the source of this universal enrichment? This book addresses those difficult questions, and offers a unique cross-disciplinary perspective on some of the most profound issues at the heart of science and philosophy. Readers will gain insights in complexity that reach deep into key areas of physics, biology, complexity science, philosophy and religion.

In this volume, which was originally published in 1996, noisy information is studied in the context of computational complexity; in other words the text deals with the computational complexity of mathematical problems for which information is partial, noisy and priced. The author develops a general theory of computational complexity of continuous problems with noisy information and gives a number of applications; deterministic as well as stochastic noise is considered. He presents optimal algorithms, optimal information, and complexity bounds in different settings: worst case, average case, mixed worst-average and average-worst, and asymptotic. The book integrates the work of researchers in such areas as computational complexity, approximation theory and statistics, and includes many fresh results as well. About two hundred exercises are supplied with a view to increasing the reader's understanding of the subject. The text will be of interest to professional computer scientists, statis

Complexity and emergence (the appearance and impact of the new) can be the bane of managers and their organizations.? Both complexity and emergence threaten to upset adherence to predefined categories

This book examines how to characterize complexity in engineering design with a specific regard to dependency modeling. It offers 52 complexity metrics that show different facets of how complexity take

Noting the increasing application of complexity science to business, Allen (evolutionary complex systems, Cranfield U., UK) et al. assemble a handbook of 36 chapters on complexity science and manageme

In this provocative and informative book, Don Norman writes that the complexity of our technology must mirror the complexity and richness of our lives. It’s not complexity that’s the problem; it’s bad

Spatial planning is about dealing with our 'everyday' environment. In A Planner's Encounter with Complexity we present various understandings of complexity and how the environment is considered accord

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.

"The Complexity of Proceduralized Tasks" deals with the problem of quantifying the complexity of a proceduralized task; in other words, a task written as a procedure. This book proposes a systematic f

The leading theme of the book is complexity in quantum dynamics. This issue is addressed by comparison with the classical ergodic, information and algorithmic complexity theories.Of particular import

Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in sc

The purpose of the science of complexity is to provide, if not a unified approach, at least useful tools to tackling complex problems in various scientific domains. Generally, complexity is considered

In Romantic Complexity, Jack Stillinger examines three of the most admired poets of English Romanticism--Keats, Coleridge, and Wordsworth--with a focus on the complexity that results from the multiple

A collection of scholarly essays, Complexity Theory and the Philosophy of Education provides an accessible theoretical introduction to the topic of complexity theory while considering its broader impl

Global Complexity is a path-breaking book, which examines how the ideas of chaos and complexity can help us to analyse global processes. Urry argues that there are major advantages in thinking about g

Global Complexity is a path-breaking book, which examines how the ideas of chaos and complexity can help us to analyse global processes. Urry argues that there are major advantages in thinking about g

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

The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.

In Complexity and Postmodernism, Paul Cilliers explores the idea of complexity in the light of contemporary perspectives from philosophy and science. Cilliers offers us a unique approach to understand

In this volume, which was originally published in 1996, noisy information is studied in the context of computational complexity; in other words the text deals with the computational complexity of mathematical problems for which information is partial, noisy and priced. The author develops a general theory of computational complexity of continuous problems with noisy information and gives a number of applications; deterministic as well as stochastic noise is considered. He presents optimal algorithms, optimal information, and complexity bounds in different settings: worst case, average case, mixed worst-average and average-worst, and asymptotic. The book integrates the work of researchers in such areas as computational complexity, approximation theory and statistics, and includes many fresh results as well. About two hundred exercises are supplied with a view to increasing the reader's understanding of the subject. The text will be of interest to professional computer scientists, statis

The first unified introduction and reference for the field of computational complexity. Virtually non-existent only 25 years ago, computational complexity has expanded tremendously and now comprises a