Recursion theory

SQL is full of difficulties and traps for the unwary. You can avoid them if you understand relational theory, but only if you know how to put the theory into practice. In this insightful book, author C.J. Date explains relational theory in depth, and demonstrates through numerous examples and exercises how you can apply it directly to your use of SQL. This second edition includes new material on recursive queries, “missing information” without nulls, new update operators, and topics such as aggregate operators, grouping and ungrouping, and view updating.
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Various feature descriptions are being employed in constrainedbased grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions considered in this paper are the possibly quantified firstorder formulae obtained from a signature of features and sorts. We establish a complete firstorder theory F T by means of three axiom schemes and construct three elementarily equivalent models. One of the models consists of socalled feature graphs, a data structure common in computational linguistics. ...
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This chapter includes contents: Kleene Star Closure, Plus operation, recursive definition of languages, INTEGER, EVEN, factorial, PALINDROME, {anbn}, languages of strings (i) ending in a, (ii) beginning and ending in same letters, (iii) containing aa or bb (iv)containing exactly aa.
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This chapter includes contents: RE, Recursive definition of RE, defining languages by RE, { x}*, { x}+, {a+b}*, language of strings having exactly one aa, Language of strings of even length, language of strings of odd length, RE defines unique language (as Remark), language of strings having at least one a, language of strings havgin at least one a and one b, Language of strings starting with aa and ending in bb, Language of strings starting with and ending in different letters.
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This chapter presents the following content: Mathematical induction, strong induction, wellordering, recursive definitions, structural induction, recursive algorithms, program correctness (not yet included in overheads).
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References Abel, Andrew B., N. Gregory Mankiw, Lawrence H. Summers, and Richard J. Zeckhauser. 1989. “Assessing Dynamic Eﬃciency: Theory and Evidence.” Review of Economic Studies, Vol. 56, pp. 1–20. Abreu, Dilip. 1988.
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This volume constitutes the Proceedings of the Third International Congress for Logic, Methodology and Philosophy of Science. The Congress was held at the Grand Hotel Krasnapolsky, Amsterdam, from August 25 to September 2, 1967, under the joint of the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science. The Congress took place in the Netherlands at the invitation of the Nederlandse Vereniging voor Logica en Wijsbegeerte der Exacte Wet enschap pen....
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Chapter 3 Dynamic Programming This chapter introduces basic ideas and methods of dynamic programming. 1 It sets out the basic elements of a recursive optimization problem, describes the functional equation (the Bellman equation), presents three methods for solving the Bellman equation
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Part III Competitive equilibria and applications Chapter 7 Recursive (Partial) Equilibrium 7.1. An equilibrium concept This chapter formulates competitive and oligopolistic equilibria in some dynamic settings. Up to now, we have studied singleagent problems where components of the state vector not under the control of the agent were taken as given.
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Chapter 12 Recursive competitive equilibria 12.1. Endogenous aggregate state variable For pure endowment stochastic economies, chapter 8 described two types of competitive equilibria, one in the style of Arrow and Debreu with markets that convene at time 0 and trade a complete set of historycontingent securities
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Part V Recursive contracts Chapter 18 Dynamic Stackelberg problems 18.1. History dependence Previous chapters described decision problems that are recursive in what we can call ‘natural’ state variables, i.e., state variables that describe stocks of capital, wealth, and information that helps forecast future values of prices and quantities
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Part VI Classical monetary economics and search Chapter 24 FiscalMonetary Theories of Inﬂation 24.1. The issues This chapter introduces some issues in monetary theory that mostly revolve around coordinating monetary and ﬁscal policies. We start from the observation that complete markets models have no role for inconvertible currency
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Chapter 19 Insurance Versus Incentives 19.1. Insurance with recursive contracts This chapter studies a planner who designs an eﬃcient contract to supply insurance in the presence of incentive constraints imposed by his limited ability either to enforce contracts or to observe households’ actions or incomes.
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Chapter 21 Optimal Unemployment Insurance 21.1. Historydependent UI schemes This chapter applies the recursive contract machinery studied in chapters 19, 20, and 22 in contexts that are simple enough that we can go a long way toward computing the optimal contracts by hand.
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Chapter 23 Two topics in international trade 23.1. Two dynamic contracting problems This chapter studies two models in which recursive contracts are used to overcome incentive problems commonly thought to occur in international trade. The ﬁrst is Andrew Atkeson’s model of lending in the context of a dynamic setting
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The Naval Facilities Engineering Command seeks to expand the technology base upon which future shore facilities are founded. An important area in which a new design approach is being developed is in the management and understanding of those characteristics of earthquake and explosively generated foundation motions that damage or destroy Naval equipment. This report is a part of the design method development. Specifically, it documents and offers a new method of shock and response spectrum computation.
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ON THE APPEARANCE OF PRIMES IN LINEAR RECURSIVE SEQUENCES JOHN H. JAROMA Received 16 August 2004 and
ON THE APPEARANCE OF PRIMES IN LINEAR RECURSIVE SEQUENCES JOHN H. JAROMA Received 16 August 2004 and in revised form 5 December 2004 We present an application of diﬀerence equations to number theory by considering the set √ √ of linear secondorder recursive relations, Un+2 ( √ R,Q) = RUn+1 − QUn , U0 = 0, U1 = 1, √ √ and Vn+2 ( R,Q) = RVn+1 − QVn , V0 = 2,V1 = R, where R and Q are relatively prime integers and n ∈ {0,1,...}. These equations describe the set of extended Lucas sequences, or rather, the Lehmer sequences. We...
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This volume constitutes the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science arranged by the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science. The logical sections of the Congress also constituted the European Logic Colloqium '91. The Congress took place in Uppsala, Sweden, from August 7 to August 14, 1991.
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StateSpace Kalman Filters 7.2 SampleAdaptive Filters y(m) e(m) µ α w(m) α z –1 wk(m+1) ADAPTIVE FILTERS 7.3 Recursive Least Square (RLS) Adaptive Filters 7.4 The SteepestDescent Method 7.5 The LMS Filter 7.6 Summary A daptive filters are used for nonstationary signals and environments, or in applications where a samplebysample adaptation of a process or a low processing delay is required.
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This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems. The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingalebased approach.
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