November 17

November 17 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing November 17, 2005
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November 17, 2005 Agenda •Today – Finish Section 7.2 – Start Section 7.3
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November 17, 2005 Announcement • Homework due next Tuesday (11/22) – 7.3 a, 7.4, 7.6 (union only), 7.9, 7.12 • 1st edition • 7.3a, 7.4, 7.6 (union only), 7.10, 7.12
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November 17, 2005 Last class • Introduced the class P –P = U k TIME(n k ) • Proved two languages are in P
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November 17, 2005 Another problem in P • RELPRIME = {<x,y> | x and y are relatively prime} •RELPRI ME P • How can we show this? –We cannot find prime factorization of x and y and compare – Use Euclidean algorithm for finding gcd(x,y) •<x ,y>
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November 17, 2005 Euclidean algorithm E = “On input <x,y>, where x and y are natural numbers in binary: 1. Repeat until y = 0 1. Assign x x mod y 2. Exchange x and y 2. Output x”
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November 17, 2005 Solution to RELPRIME R = “On input <x,y>, where x and y are natural numbers in binary: 1. Run E on <x,y> 2. If result is 1, accept 3. Else reject
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November 17 - CSCI 2670 Introduction to Theory of Computing...

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