Boolean Function Complexity

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

This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability (created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages). These are addressed from the classical perspective of their generation by grammars and from the modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account by one of the leading lights of the subject will prove exceptionally useful reading for graduate students, and researchers in theoretical computer science and mathematics.

Introduction to Mathematical Logic Resolution Principle, Second Edition, in nine chapters, discusses Boolean algebra theory, propositional calculus and predicated calculus theory, resolution principl

What do traffic jams, stock market crashes, and wars have in common? They are all explained using complexity, an unsolved puzzle that many researchers believe is the key to predicting - and ultimately

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 existence and functioning of intrinsically disordered proteins (IDPs) challenge the classical structure-function paradigm that equates function with a well-defined 3D structure. Uncovering the dis

Complete review of pulmonary function tests in clinical practice, including performance and interpretation of lung function tests with an emphasis on practical aspects. Review of polysomnographic tech

"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

By now, most academics have heard something about the new science of complexity. In a manner reminiscent of Einstein and the last hundred years of physics, complexity science has captured the public i

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

This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta function

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

When the term "complexity" appears in architectural contexts, it is clear at once that it has more than one definition, more than one interpretation, more than one architectural conceptualization. Per

Reflecting current practice with a renewed focus on function-based assessments and evidence-based interventions, Cognitive and Perceptual Rehabilitation: Optimizing Function includes all of the tools

This book collects survey papers in the fields of entropy, search and complexity, summarizing the latest developments in their respective areas. More than half of the papers belong to search theory wh

Fusing two key concerns of contemporary sociology: globalization and its discontents, and the 'complexity turn' in social theory, authors Chesters and Welsh utilize complexity theory to analyze the sh

Human Hand Function is a multidisciplinary book that reviews the sensory and motor aspects of normal hand function from both neurophysiological and behavioral perspectives. Lynette Jones and Susan Led

The only text to cover lung function assessment from first principles including methodology, reference values and interpretationNew for this edition:- More illustrations to convey concepts clearly to

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

Modern cryptology increasingly employs mathematically rigorous concepts and methods from complexity theory. Conversely, current research topics in complexity theory are often motivated by questions an

Proteins: Structure and Function is a comprehensive introduction to the study of proteins and their importance to modern biochemistry. Each chapter addresses the structure and function of proteins wi

This undergraduate-level describes the mathematics most needed in computer science. Bender and Williamson (both mathematics, U. of California, San Diego) cover Boolean functions and computer arithmeti

A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students a

We live in a moment of unprecedented complexity, an era in which change and information can move faster than our ability to comprehend them. With The Moment of Complexity, Mark C. Taylor offers a map

Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous sys

The science of complexity is concerned with the study of complex, adaptive systems. Its insights have in recent decades been applied with gusto by social scientists and other thinkers.As research in a

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

The two internationally renowned authors elucidate the structure of "fast" parallel computation. Its complexity is emphasised through a variety of techniques ranging from finite combinatorics, probabi

The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal t

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

Neurotransmitters, Drugs and Brain Function aims to link basic aspects of the activity of neurotransmitters at the receptor and synaptic level with their role in normal brain function, disease states,

A groundbreaking look at complexity theory and its implications in the world of finance Complexity theory tells us that processes with a large number of seemingly independent agents-such as free marke

Skeletal Muscle Mechanics: From Mechanisms to Function summarises the variety of approaches used by today's scientist to understand muscle function and the mechanisms of contraction. This book contain