lecture30 - Semi-structured or Web-like Databases CS30785...

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Semi-structured or Web-like Databases CS30785 Lecture 30 – Recursive Theory Dr. Gangmin Gary Li Department of CSSE XJTLU [email protected] Room: D441
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2 Previous lecture • Graph Decoration of hyperset D G ( v ) • Decoration operations and its semantics • Recursive -Separation * Δ L30 –Recursive theory CS30785 - Semistructured or Web-like databases
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3 Outline • Recursive theory - Can R* be defined by R? L30 –Recursive theory CS30785 - Semistructured or Web-like databases
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Recursion in Real Life • Two basic rules of recursion – A simple base case (or cases), and – A set of rules which reduce all other cases toward the base case. • E.g. – One's parents are one's ancestors ( base case ). – The parents of one's ancestors are also one's ancestors ( recursion step ). L30 –Recursive theory CS30785 - Semistructured or Web-like databases 4
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Examples • How do you move a stack of 100 boxes? • 1 is a natural number, and each natural number has a successor, which is also a natural number. 1 is in N . If an element n is in N then n +1 is in N . To understand recursion, you must first understand recursion L30 –Recursive theory CS30785 - Semistructured or Web-like databases 5
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L30 –Recursive theory CS30785 - Semistructured or Web-like databases 6
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L30 –Recursive theory CS30785 - Semistructured or Web-like databases 7 The basic Recursion theorem Given a set X , an element a of X and a function the theorem states that there is a unique function (where denotes the set of natural numbers including zero) such that F (0) = a F ( n + 1) = f ( F ( n )) for any natural number n .
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Proof by Mathematical Induction L30 –Recursive theory CS30785 - Semistructured or Web-like databases 8
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9 L30 –Recursive theory CS30785 - Semistructured or Web-like databases
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10 L30 –Recursive theory CS30785 - Semistructured or Web-like databases
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L30 –Recursive theory CS30785 - Semistructured or Web-like databases
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This note was uploaded on 05/22/2011 for the course CS 30785 taught by Professor Garyli during the Spring '11 term at University of Liverpool.

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lecture30 - Semi-structured or Web-like Databases CS30785...

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