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Descriptive Complexity

Author: Neil Immerman

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 275

ISBN-13: 1461205395

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.

Descriptive Complexity, Canonisation, and Definable Graph Structure Theory

Author: Martin Grohe

Publisher: Cambridge University Press

Published: 2017-08-17

Total Pages: 554

ISBN-13: 1108234305

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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 The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.

Descriptive Set Theoretic Methods in Automata Theory

Author: Michał Skrzypczak

Publisher: Springer

Published: 2016-08-05

Total Pages: 211

ISBN-13: 3662529475

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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.

Linguistic Complexity

Author: Bernd Kortmann

Publisher: Walter de Gruyter

Published: 2012-05-29

Total Pages: 272

ISBN-13: 3110229226

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Linguistic complexity is one of the currently most hotly debated notions in linguistics. The essays in this volume reflect the intricacies of thinking about the complexity of languages and language varieties (here: of English) in three major contact-related fields of (and schools in) linguistics: creolistics, indigenization and nativization studies (i.e. in the realm of English linguistics, the “World Englishes” community), and Second Language Acquisition (SLA) research: How can we adequately assess linguistic complexity? Should we be interested in absolute complexity or rather relative complexity? What is the extent to which language contact and/or (adult) language learning might lead to morphosyntactic simplification? The authors in this volume are all leading linguists in different areas of specialization, and they were asked to elaborate on those facets of linguistic complexity which are most relevant in their area of specialization, and/or which strike them as being most intriguing. The result is a collection of papers that is unique in bringing together leading representatives of three often disjunct fields of linguistic scholarship in which linguistic complexity is seen as a dynamic and inherently variable parameter.

The Register-Functional Approach to Grammatical Complexity

Author: Douglas Biber

Publisher: Routledge

Published: 2021-12-31

Total Pages: 528

ISBN-13: 1000481921

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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.

Computational Complexity

Author: Sanjeev Arora

Publisher: Cambridge University Press

Published: 2009-04-20

Total Pages: 609

ISBN-13: 0521424267

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New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Descriptive Complexity, Canonisation, and Definable Graph Structure Theory

Author: Martin Grohe

Publisher: Cambridge University Press

Published: 2017-08-17

Total Pages: 554

ISBN-13: 1107014522

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

Complexity and Education

Author: Brent Davis

Publisher: Routledge

Published: 2014-06-03

Total Pages: 215

ISBN-13: 1134815786

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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.

Finite Model Theory and Its Applications

Author: Erich Grädel

Publisher: Springer Science & Business Media

Published: 2007-06-04

Total Pages: 447

ISBN-13: 3540688048

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Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.

Complexity and Postmodernism

Author: Paul Cilliers

Publisher: Routledge

Published: 2002-09-11

Total Pages: 170

ISBN-13: 1134743297

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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.