'Induction hypothesis' diaporamas de présentation

Induction: One Step At A Time

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NFAs accept the Regular Languages

NFAs accept the Regular Languages. Equivalence of Machines. Definition: Machine is equivalent to machine if. Example of equivalent machines. NFA. FA. We will prove:. Languages accepted by NFAs. Regular Languages. Languages accepted by FAs. NFAs and FAs have the

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15-251

15-251. Some. Great Theoretical Ideas in Computer Science. for. Inductive Reasoning. Lecture 4 (January 24, 2008). Dominoes. Domino Principle: Line up any number of dominos in a row; knock the first one over and they will all fall.

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General Announcements

General Announcements. Project Due Friday, 1/30 Labs start Wednesday & Thursday Java review Weiss 1.19, 1.20 You may show up & hand in Workshops start Sunday Why do we do workshops. WORKSHOPS.

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CS2210:0001Discrete Structures Induction and Recursion

CS2210:0001Discrete Structures Induction and Recursion. Fall 2017 Sukumar Ghosh. What is mathematical induction?. It is a method of proving that something holds. Suppose we have an infinite ladder , and we want to know if we can reach every step on this ladder.

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Advanced Algebraic Algorithms on Integers and Polynomials

Advanced Algebraic Algorithms on Integers and Polynomials. Analysis of Algorithms. Prepared by John Reif, Ph.D. Integer and Polynomial Computations. Newton Iteration: application to division Evaluation and Interpolation via Chinese Remaindering Main Lecture Material:

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THE LIST COLORING CONJECTURE

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David Evans http://www.cs.virginia.edu/evans

Lecture 11: Parsimonious Parsing. David Evans http://www.cs.virginia.edu/evans. cs302: Theory of Computation University of Virginia Computer Science. Menu. Fix proof from last class Interpretive Dance! Parsimonious Parsing (Parsimoniously). PS3 Comments Available Today

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Proofs Gone Wrong: A Lecture On Mathematical Writing

Proofs Gone Wrong: A Lecture On Mathematical Writing. CSC373, Winter 2007. Why care about writing?. Right Idea, bad proof: gets a 50 Your proof is a method of persuading the reader that something is true. Errors in logic love to hide behind bad writing. Toy Problem.

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MA/CSSE 474

MA/CSSE 474. Theory of Computation. Regular Expressions Intro. Your Questions?. Still more language ambiguity!. Previous class days' material Reading Assignments. HW5 problems Anything else. Regular Languages. Regular Language. Describes. Regular Expression. Accepts.

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CS201: Data Structures and Discrete Mathematics I

CS201: Data Structures and Discrete Mathematics I. Mathematical Induction. Outline. Proof techniques Inductive proofs and examples. Proof Techniques. There are a number of techniques to prove or to disprove an conjecture. Disproof by counterexample Exhaustive proof Direct proof

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Analysis of Algorithms CS 477/677

Analysis of Algorithms CS 477/677. Instructor: Monica Nicolescu Lecture 4. Methods for Solving Recurrences. Iteration method Substitution method Recursion tree method Master method. The recursion-tree method. Convert the recurrence into a tree:

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Chapter 6

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Chapter 7

Chapter 7. Recursion. Recurrent Sequence. A recursively defined sequence First, certain initial values are specified ? c.f., base condition Later terms of the sequence are defined by relating them to earlier terms ?c.f., recursive function calls Example

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Mathematical Induction

Mathematical Induction. What it is? Why is it a legitimate proof method? How to use it?. Important Sets of Integers. Z all integers (whole numbers) Z + the positive integers Z - the negative integers N Natural numbers: non-negative integers

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The Cocke-Kasami-Younger Algorithm

The Cocke-Kasami-Younger Algorithm. An example of a CFG in CNF. An example of bottom-up parsing, for CFG in Chomsky normal form. G : S ? AB | BB A ? CC | AB | a B ? BB | CA | b C ? BA | AA | b. 2 possibilities for first production. S. S. S. B. B. A. A. B. A.

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Induction

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Review of Inductive Construction of Sets and Inductive Proof Techniques

Review of Inductive Construction of Sets and Inductive Proof Techniques. Example 1.1, page 5: Power Set Construction. Let S = {a, b, c}. Power Set The set of all the subsets of a given set S, is called power set of S. The power set of S is denoted by p (S) or 2 |S| . p (S) = { ? }.

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Key Answers for Homework #1

3 . (1) Base: When there is one node. To have a path, there should be an edge, which is self-loop as shown below. Obviously, a path of length greater than or equal to one has a cycle. 1. 1. 1. 2. 1. 1. 2. Figure (a) Odd case. Figure (b) Even case. Key Answers for Homework #1.

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