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High Quality Content by WIKIPEDIA articles! The language TQBF is a formal language in computer science that contains True Quantified Boolean Formulas. A fully quantified boolean formula is a formula in first-order logic where every variable is quantified (or bound), using either existential or universal quantifiers, at the beginning of the sentence. Any such formula is always either true or false (since there are no free variables). If such a formula evaluates to true, then that formula is in the language TQBF. It is also known as QSAT (Quantified SAT). In computational complexity theory, the quantified Boolean formula problem (QBF) is a generalization of the Boolean satisfiability problem in which both existential quantifiers and universal quantifiers can be applied to each variable.

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Although they are believed to be unsolvable in general, tractability results suggest that some practical NP-hard problems can be efficiently solved. Combinatorial search algorithms are designed to efficiently explore the usually large solution space of these instances by reducing the search space to feasible regions and using heuristics to efficiently explore these regions. Various mathematical formalisms may be used to express and tackle combinatorial problems, among them the constraint satisfaction problem (CSP) and the propositional satisfiability problem (SAT). These algorithms, or constraint solvers, apply search space reduction through inference techniques, use activity-based heuristics to guide exploration, diversify the searches through frequent restarts, and often learn from their mistakes.In this book the author focuses on knowledge sharing in combinatorial search, the capacity to generate and exploit meaningful information, such as redundant constraints, heuristic hints, and performance measures, during search, which can dramatically improve the performance of a constraint solver. Information can be shared between multiple constraint solvers simultaneously working on the same instance, or information can help achieve good performance while solving a large set of related instances. In the first case, information sharing has to be performed at the expense of the underlying search effort, since a solver has to stop its main effort to prepare and communicate the information to other solvers, on the other hand, not sharing information can incur a cost for the whole system, with solvers potentially exploring unfeasible spaces discovered by other solvers. In the second case, sharing performance measures can be done with little overhead, and the goal is to be able to tune a constraint solver in relation to the characteristics of a new instance - this corresponds to the selection of the most suitable algorithm for solving a given instance.The book is suitable for researchers, practitioners, and graduate students working in the areas of optimization, search, constraints, and computational complexity.

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If you know how to program with Python and also know a little about probability, you’re ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you’ll begin to apply these techniques to real-world problems.Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book’s computational approach helps you get a solid start.* Use your existing programming skills to learn and understand Bayesian statistics* Work with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testing* Get started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockey* Learn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome.

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Although they are believed to be unsolvable in general, tractability results suggest that some practical NP-hard problems can be efficiently solved. Combinatorial search algorithms are designed to efficiently explore the usually large solution space of these instances by reducing the search space to feasible regions and using heuristics to efficiently explore these regions. Various mathematical formalisms may be used to express and tackle combinatorial problems, among them the constraint satisfaction problem (CSP) and the propositional satisfiability problem (SAT). These algorithms, or constraint solvers, apply search space reduction through inference techniques, use activity-based heuristics to guide exploration, diversify the searches through frequent restarts, and often learn from their mistakes. In this book the author focuses on knowledge sharing in combinatorial search, the capacity to generate and exploit meaningful information, such as redundant constraints, heuristic hints, and performance measures, during search, which can dramatically improve the performance of a constraint solver. Information can be shared between multiple constraint solvers simultaneously working on the same instance, or information can help achieve good performance while solving a large set of related instances. In the first case, information sharing has to be performed at the expense of the underlying search effort, since a solver has to stop its main effort to prepare and communicate the information to other solvers; on the other hand, not sharing information can incur a cost for the whole system, with solvers potentially exploring unfeasible spaces discovered by other solvers. In the second case, sharing performance measures can be done with little overhead, and the goal is to be able to tune a constraint solver in relation to the characteristics of a new instance &#8211; this corresponds to the selection of the most suitable algorithm for solving a given instance. The book is suitable for researchers, practitioners, and graduate students working in the areas of optimization, search, constraints, and computational complexity.

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The NP-completeness of SAT is a celebrated example of the power of bounded-depth computation: the core of the argument is a depth reduction establishing that any small nondeterministic circuit - an arbitrary NP computation on an arbitrary input - can be simulated by a small non deterministic circuit of depth 2 with unbounded fan-in - a SAT instance. Many other examples permeate theoretical computer science. On the Power of Small-Depth Computation discusses a selected subset of them, and includes a few unpublished proofs. On the Power of Small-Depth Computation starts with a unified treatment of the challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over . It goes on to describe an unpublished proof that small bounded-depth circuits (AC°) have exponentially small correlation with the parity function. The proof is due to Adam Klivans and Salil Vadhan; it builds upon and simplifies previous ones. Thereafter, it looks at a depth-reduction result by Leslie Valiant, the proof of which has not before appeared in full. It concludes by presenting the result by Benny Applebaum, Yuval Ishai, and Eyal Kushilevitz that shows that, under standard complexity theoretic assumptions, many cryptographic primitives can be implemented in very restricted computational models. On the Power of Small-Depth Computation is an ideal primer for anyone with an interest in computational complexity, random structures and algorithms and theoretical computer science generally.

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Hybrid Optimization focuses on the application of artificial intelligence and operations research techniques to constraint programming for solving combinatorial optimization problems. This book covers the most relevant topics investigated in the last ten years by leading experts in the field, and speculates about future directions for research. This book includes contributions by experts from different but related areas of research including constraint programming, decision theory, operations research, SAT, artificial intelligence, as well as others. These diverse perspectives are actively combined and contrasted in order to evaluate their relative advantages. This volume presents techniques for hybrid modeling, integrated solving strategies including global constraints, decomposition techniques, use of relaxations, and search strategies including tree search local search and metaheuristics. Various applications of the techniques presented as well as supplementary computational tools are also discussed.

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Anbieter: Thalia AT

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If you know how to program with Python and also know a little about probability, you&#8217;re ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you&#8217;ll begin to apply these techniques to real-world problems. Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book&#8217;s computational approach helps you get a solid start. * Use your existing programming skills to learn and understand Bayesian statistics * Work with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testing * Get started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockey * Learn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome.

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This dynamic reference work provides solutions to vital algorithmic problems for scholars, researchers, practitioners, teachers and students in fields such as computer science, mathematics, statistics, biology, economics, financial software, and medical informatics. This second edition is broadly expanded, building upon the success of its former edition with more than 450 new and updated entries. These entries are designed to ensure algorithms are presented from growing areas of research such as bioinformatics, combinatorial group testing, differential privacy, enumeration algorithms, game theory, massive data algorithms, modern learning theory, social networks, and VLSI CAD algorithms. Over 630 entries are organized alphabetically by problem, with subentries allowing for distinct solutions. Each entry includes a description of the basic algorithmic problem; the input and output specifications; key results; examples of applications; citations to key literature, open problems, experimental results, links to data sets and downloadable code. All entries are peer-reviewed, written by leading experts in the field&#8212;and each entry contains links to a summary of the author&#8217;s research work. This defining reference is available in both print and online&#8212;a dynamic living work with hyperlinks to related entries, cross references citations, and a myriad other valuable URLs. New and Updated entries include: Algorithmic Aspects of Distributed Sensor Networks, Algorithms for Modern Computers Bioinformatics Certified Reconstruction and Mesh Generation Combinatorial Group Testing Compression of Text and Data Structures Computational Counting Computational Economics Computational Geometry Differential Privacy Enumeration Algorithms Exact Exponential Algorithms Game Theory Graph Drawing Group Testing Internet Algorithms Kernels and Compressions Massive Data Algorithms Mathematical Optimization Modern Learning Theory Social Networks Stable Marriage Problems, k-SAT Algorithms Sublinear Algorithms Tile Self-Assembly VLSI CAD Algorithms

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