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In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.
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This volume explores play from an interdisciplinary standpoint. In seeking to encourage innovative and in-depth trans-disciplinary dialogues, contributions hosted in this volume succeed in revealing research realities and avenues concerning the study of play. With input from a variety of areas, i.e. sociology, technology, creative arts, history, and philosophy, this volume is a must-have for anyone with an interest in looking into the study of play from a multi-disciplinary angle.
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Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.
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Das Lehrbuch enthält die wesentlichen Grundzüge der Theoretischen Informatik. Es gibt eine verständliche Einführung in die Gebiete Berechenbarkeits-, Automatentheorie, Formale Sprachen und Komplexitätstheorie. Alle Zusammenhänge sind verständlich bewiesen und durch Beispiele untermauert. Von praktischer Bedeutung sind Untersuchungen zur Existenz von nicht entscheidbaren und nicht effizient lösbaren Problemen. Es erfolgt eine Einführung in die Theorie der NP-Vollständigkeit mit Beispielen. Eine Vielzahl von Übungsaufgaben, sämtlich mit ausführlichen Lösungen, die zum Selbsttest wie auch zur Vorbereitung auf den studentischen Übungsbetrieb geeignet sind.
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