By virtue of the close relationship between logic and relational databases, it turns out that complexity has important applications to databases such as analyzing the parallel time needed to compute a query, and the analysis of nondeterministic classes. This book is a relatively self-contained introduction to the subject, which includes the necessary background material, as well as numerous examples and exercises.

From the Preface: We hope that this small volume will suggest directions of synergy and contact for future researchers to build upon, creating connections and making discoveries that will help explain some of the many mysteries of computation. Finite model theory can be succinctly described as the study of logics on finite structures. It is an area of research existing between mathematical logic and computer science. This area has been developing through continuous interaction with computational complexity, database theory, and combinatorics. The volume presents articles by leading researchers who delivered talks at the "Workshop on Finite Models and Descriptive Complexity" at Princeton in January 1996 during a DIMACS sponsored Special Year on Logic and Algorithms. Each article is self-contained and provides a valuable introduction to the featured research areas connected with finite model theory. This text will also be of interest to those working in discrete mathematics and combinatorics.

This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.

This collection brings together the authors' previous research with new work on the Register-Functional (RF) approach to grammatical complexity, offering a unified theoretical account for its further study. The book traces the development of the RF approach from its foundations in two major research strands of linguistics: the study of sociolinguistic variation and the text-linguistic study of register variation. Building on this foundation, the authors demonstrate the RF framework at work across a series of corpus-based research studies focused specifically on grammatical complexity in English. The volume highlights early work exploring patterns of grammatical complexity in present-day spoken and written registers as well as subsequent studies which extend this research to historical patterns of register variation and the application of RF research to the study of writing development for L1 and L2 English university students. Taken together, along with the addition of introductory chapters connecting the different studies, the volume offers readers with a comprehensive resource to better understand the RF approach to grammatical complexity and its implications for future research. The volume will appeal to students and scholars with research interests in either descriptive linguistics or applied linguistics, especially those interested in grammatical complexity and empirical, corpus-based approaches.

The book is based on the PhD thesis “Descriptive Set Theoretic Methods in Automata Theory,” awarded the E.W. Beth Prize in 2015 for outstanding dissertations in the fields of logic, language, and information. The thesis reveals unexpected connections between advanced concepts in logic, descriptive set theory, topology, and automata theory and provides many deep insights into the interplay between these fields. It opens new perspectives on central problems in the theory of automata on infinite words and trees and offers very impressive advances in this theory from the point of view of topology. "...the thesis of Michał Skrzypczak offers certainly what we expect from excellent mathematics: new unexpected connections between a priori distinct concepts, and proofs involving enlightening ideas.” Thomas Colcombet.

This book explores the contributions, actual and potential, of complexity thinking to educational research and practice. While its focus is on the theoretical premises and the methodology, not specific applications, the aim is pragmatic--to present complexity thinking as an important and appropriate attitude for educators and educational researchers. Part I is concerned with global issues around complexity thinking, as read through an educational lens. Part II cites a diversity of practices and studies that are either explicitly informed by or that might be aligned with complexity research, and offers focused and practiced advice for structuring projects in ways that are consistent with complexity thinking. Complexity thinking offers a powerful alternative to the linear, reductionist approaches to inquiry that have dominated the sciences for hundreds of years and educational research for more than a century. It has captured the attention of many researchers whose studies reach across traditional disciplinary boundaries to investigate phenomena such as: How does the brain work? What is consciousness? What is intelligence? What is the role of emergent technologies in shaping personalities and possibilities? How do social collectives work? What is knowledge? Complexity research posits that a deep similarity among these phenomena is that each points toward some sort of system that learns. The authors’ intent is not to offer a complete account of the relevance of complexity thinking to education, not to prescribe and delimit, but to challenge readers to examine their own assumptions and theoretical commitments--whether anchored by commonsense, classical thought or any of the posts (such as postmodernism, poststructuralism, postcolonialism, postpositivism, postformalism, postepistemology) that mark the edges of current discursive possibility. Complexity and Education is THE introduction to the emerging field of complexity thinking for the education community. It is specifically relevant for educational researchers, graduate students, and inquiry-oriented teacher practitioners.

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 understanding complexity and computational theory by integrating postmodern theory (like that of Derrida and Lyotard) into his discussion. Complexity and Postmodernism is an exciting and an original book that should be read by anyone interested in gaining a fresh understanding of complexity, postmodernism and connectionism.

This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.

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 produce dynamic patterns and structures. Diversity plays a different role in a complex system than it does in an equilibrium system, where it often merely produces variation around the mean for performance measures. In complex adaptive systems, diversity makes fundamental contributions to system performance. Scott Page gives a concise primer on how diversity happens, how it is maintained, and how it affects complex systems. He explains how diversity underpins system level robustness, allowing for multiple responses to external shocks and internal adaptations; how it provides the seeds for large events by creating outliers that fuel tipping points; and how it drives novelty and innovation. Page looks at the different kinds of diversity--variations within and across types, and distinct community compositions and interaction structures--and covers the evolution of diversity within complex systems and the factors that determine the amount of maintained diversity within a system. Provides a concise and accessible introduction Shows how diversity underpins robustness and fuels tipping points Covers all types of diversity The essential primer on diversity in complex adaptive systems

This collection of newly comissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Presents controversies in philosophical implications and applications of formal symbolic logic. Surveys major trends and offers original insights.