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This advanced textbook presents a broad and up-to-date view of the computational complexity theory of Boolean circuits. It combines the algorithmic and the computability-based approach, and includes extensive discussion of the literature to facilitate further study. It begins with efficient Boolean circuits for problems with high practical relevance, e.g., arithmetic operations, sorting, and transitive closure, then compares the computational model of Boolean circuits with other models such as Turing machines and parallel machines. Examination of the complexity of specific problems leads to the definition of complexity classes. The theory of circuit complexity classes is then thoroughly developed, including the theory of lower bounds and advanced topics such as connections to algebraic structures and to finite model theory.

Computer science --- Algebra, Boolean. --- Computational complexity. --- Electronic digital computers --- Logic, Symbolic and mathematical. --- Circuits --- Design. --- Computers. --- Algorithms. --- Mathematical logic. --- Computer mathematics. --- Electronics. --- Microelectronics. --- Theory of Computation. --- Computation by Abstract Devices. --- Algorithm Analysis and Problem Complexity. --- Mathematical Logic and Formal Languages. --- Computational Mathematics and Numerical Analysis. --- Electronics and Microelectronics, Instrumentation. --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Electronics --- Microtechnology --- Semiconductors --- Miniature electronic equipment --- Electrical engineering --- Physical sciences --- Computer mathematics --- Electronic data processing --- Mathematics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algorism --- Algebra --- Arithmetic --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Foundations --- Automatic digital computers --- Computers, Electronic digital --- Digital computers, Electronic --- Computers --- Hybrid computers --- Sequential machine theory

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In this volume, different aspects of logics for dependence and independence are discussed, including both the logical and computational aspects of dependence logic, and also applications in a number of areas, such as statistics, social choice theory, databases, and computer security. The contributing authors represent leading experts in this relatively new field, each of whom was invited to write a chapter based on talks given at seminars held at the Schloss Dagstuhl Leibniz Center for Informatics in Wadern, Germany (in February 2013 and June 2015) and an Academy Colloquium at the Royal Netherlands Academy of Arts and Sciences (March 2014). Altogether, these chapters provide the most up-to-date look at this developing and highly interdisciplinary field and will be of interest to a broad group of logicians, mathematicians, statisticians, philosophers, and scientists. Topics covered include a comprehensive survey of many propositional, modal, and first-order variants of dependence logic; new results concerning expressive power of several variants of dependence logic with different sets of logical connectives and generalized dependence atoms; connections between inclusion logic and the least-fixed point logic; an overview of dependencies in databases by addressing the relationships between implication problems for fragments of statistical conditional independencies, embedded multivalued dependencies, and propositional logic; various Markovian models used to characterize dependencies and causality among variables in multivariate systems; applications of dependence logic in social choice theory; and an introduction to the theory of secret sharing, pointing out connections to dependence and independence logic.

Mathematics. --- Logic. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Math --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Methodology --- Computer science. --- Informatics

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In this volume, different aspects of logics for dependence and independence are discussed, including both the logical and computational aspects of dependence logic, and also applications in a number of areas, such as statistics, social choice theory, databases, and computer security. The contributing authors represent leading experts in this relatively new field, each of whom was invited to write a chapter based on talks given at seminars held at the Schloss Dagstuhl Leibniz Center for Informatics in Wadern, Germany (in February 2013 and June 2015) and an Academy Colloquium at the Royal Netherlands Academy of Arts and Sciences (March 2014). Altogether, these chapters provide the most up-to-date look at this developing and highly interdisciplinary field and will be of interest to a broad group of logicians, mathematicians, statisticians, philosophers, and scientists. Topics covered include a comprehensive survey of many propositional, modal, and first-order variants of dependence logic; new results concerning expressive power of several variants of dependence logic with different sets of logical connectives and generalized dependence atoms; connections between inclusion logic and the least-fixed point logic; an overview of dependencies in databases by addressing the relationships between implication problems for fragments of statistical conditional independencies, embedded multivalued dependencies, and propositional logic; various Markovian models used to characterize dependencies and causality among variables in multivariate systems; applications of dependence logic in social choice theory; and an introduction to the theory of secret sharing, pointing out connections to dependence and independence logic.

Mathematical logic --- Logic --- Mathematics --- wiskunde --- logica

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Hinter vielen Programmen stecken clevere Verfahren, die man als Algorithmen bezeichnet. Algorithmen lösen nicht nur mathematische Aufgaben, die sich mit Zahlen beschäftigen, sondern auch andere, ganz alltägliche Problemstellungen, bei denen logischer Spürsinn, räumliche Orientierung oder geschicktes Verhandeln gefragt sind, beispielsweise: Wie lässt sich der kürzeste Weg zwischen zwei Orten ermitteln? Wie sollten Seeräuber eine Schatzkarte aufteilen, bzw. Bankangestellte den Geheimcode des Tresors? Wie können mehrere hungrige Partygäste einen Kuchen gerecht untereinander aufteilen? Dieses Buch vollführt einen Streifzug durch die faszinierende Welt der Algorithmen. Es verlangt keine Vorkenntnisse, so dass Schüler ab der Mittelstufe und Informatik-interessierte Laien neue und überraschende Einblicke gewinnen können. In 43 Artikeln von Informatikern, die an Universitäten im In- und Ausland lehren, werden wichtige und besonders elegante Algorithmen anschaulich und umgangssprachlich erklärt.

Computers. --- Algorithms. --- Theory of Computation. --- Algorithm Analysis and Problem Complexity.

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Complex analysis --- Discrete mathematics --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- discrete wiskunde --- complexe analyse (wiskunde) --- grafische vormgeving --- informatica --- database management --- programmatielogica --- KI (kunstmatige intelligentie) --- robots --- numerieke analyse --- AI (artificiële intelligentie)