This compilation of original research articles highlight the important cross-regional, cross-chronological, and comparative approaches to political and economic landscapes in ancient South Asia and it
This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and
This book is concerned with the relationship between semantics and surface structure and in particular with the way in which each is mapped into the other. Jim Miller argues that semantic and syntactic structure require different representations and that semantic structure is far more complex than many analysts realise. He argues further that semantic structure should be based on notions of location and movement. The need for a semantic component of greater complexity is demonstrated by an examination of prepositions, particles, adverbs and verb-prefixes, and is shown to accord with cross-language and historical facts. The volume goes on to consider the sort of rules that are required to map semantic structures onto syntax. Semantics and Syntax tackles fundamental issues and draws together many of the key concepts of traditional grammar and formal linguistics. The general framework for handling syntax, semantics and morphology that it outlines is perhaps a controversial one, but it wil
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
Fritjof Capra, bestselling author of The Tao of Physics and The Web of Life, here explores another frontier in the human significance of scientific ideas—applying complexity theory to large-scale soci
This book designed to help readers develop and maintain logical, adaptable solutions to business problems. It demonstrates how to visualize these business dependencies connections with a square spread
Fascinating connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Automata can be used in group theory to encode complexity, to represent aspects of underlying geometry on a space on which a group acts, and to provide efficient algorithms for practical computation. There are also many applications in geometric group theory. The authors provide background material in each of these related areas, as well as exploring the connections along a number of strands that lead to the forefront of current research in geometric group theory. Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group. This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research students in (geometric) group theory.
Fascinating connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Automata can be used in group theory to encode complexity, to represent aspects of underlying geometry on a space on which a group acts, and to provide efficient algorithms for practical computation. There are also many applications in geometric group theory. The authors provide background material in each of these related areas, as well as exploring the connections along a number of strands that lead to the forefront of current research in geometric group theory. Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group. This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research students in (geometric) group theory.
An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophyMathematics an
Terrorism has long been a major shaping force in the world. However, the meanings of terrorism, as a word and as a set of actions, are intensely contested. This volume explores how literature has dealt with terrorism from the Renaissance to today, inviting the reader to make connections between older instances of terrorism and contemporary ones, and to see how the various literary treatments of terrorism draw on each other. The essays demonstrate that the debates around terrorism only give the fictive imagination more room, and that fiction has a great deal to offer in terms of both understanding terrorism and our responses to it. Written by historians and literary critics, the essays provide essential knowledge to understand terrorism in its full complexity. As befitting a global problem, this book brings together a truly international group of scholars, with representatives from America, Scotland, Canada, New Zealand, Italy, Israel, and other countries.
This collection of papers presents a series of in-depth examinations of a variety of advanced topics related to Boolean functions and expressions. The chapters are written by some of the most prominent experts in their respective fields and cover topics ranging from algebra and propositional logic to learning theory, cryptography, computational complexity, electrical engineering, and reliability theory. Beyond the diversity of the questions raised and investigated in different chapters, a remarkable feature of the collection is the common thread created by the fundamental language, concepts, models, and tools provided by Boolean theory. Many readers will be surprised to discover the countless links between seemingly remote topics discussed in various chapters of the book. This text will help them draw on such connections to further their understanding of their own scientific discipline and to explore new avenues for research.
The problem of inducing, learning or inferring grammars has been studied for decades, but only in recent years has grammatical inference emerged as an independent field with connections to many scientific disciplines, including bio-informatics, computational linguistics and pattern recognition. This book meets the need for a comprehensive and unified summary of the basic techniques and results, suitable for researchers working in these various areas. In Part I, the objects of use for grammatical inference are studied in detail: strings and their topology, automata and grammars, whether probabilistic or not. Part II carefully explores the main questions in the field: What does learning mean? How can we associate complexity theory with learning? In Part III the author describes a number of techniques and algorithms that allow us to learn from text, from an informant, or through interaction with the environment. These concern automata, grammars, rewriting systems, pattern languages or tra
Intended for researchers and graduate students in theoretical computer science and mathematical logic, this volume contains accessible surveys by leading researchers from areas of current work in logical aspects of computer science, where both finite and infinite model-theoretic methods play an important role. Notably, the articles in this collection emphasize points of contact and connections between finite and infinite model theory in computer science that may suggest new directions for interaction. Among the topics discussed are: algorithmic model theory, descriptive complexity theory, finite model theory, finite variable logic, model checking, model theory for restricted classes of finite structures, and spatial databases. The chapters all include extensive bibliographies facilitating deeper exploration of the literature and further research.
This book uses evolution as the unifying theme to trace the connections between levels of biological complexity from genes through nervous systems, animal societies, and human cultures. It examines t
In the field of postcolonial studies, the full richness and complexity of the connections between literature, history and ideology are often overlooked by critics hurrying to stake out their political
A comprehensive re-evaluation of Isaac Barrow (1630–1677), one of the more prominent and intriguing of all seventeenth-century men of science. Barrow is remembered today - if at all - only as Sir Isaac Newton's mentor and patron, but he in fact made important contributions to the disciplines of optics and geometry. Moreover, he was a prolific and influential preacher as well as a renowned classical scholar. By seeking to understand Barrow's mathematical work, primarily within the confines of the pre-Newtonian scientific framework, the book offers a substantial rethinking of his scientific acumen. In addition to providing a biographical study of Barrow, it explores the intimate connections among his scientific, philological and religious worldviews in an attempt to convey the complexity of the seventeenth-century culture that gave rise to Isaac Barrow, a breed of polymath that would become increasingly rare with the advent of modern science.
A comprehensive re-evaluation of Isaac Barrow (1630–1677), one of the more prominent and intriguing of all seventeenth-century men of science. Barrow is remembered today - if at all - only as Sir Isaac Newton's mentor and patron, but he in fact made important contributions to the disciplines of optics and geometry. Moreover, he was a prolific and influential preacher as well as a renowned classical scholar. By seeking to understand Barrow's mathematical work, primarily within the confines of the pre-Newtonian scientific framework, the book offers a substantial rethinking of his scientific acumen. In addition to providing a biographical study of Barrow, it explores the intimate connections among his scientific, philological and religious worldviews in an attempt to convey the complexity of the seventeenth-century culture that gave rise to Isaac Barrow, a breed of polymath that would become increasingly rare with the advent of modern science.
