Chapter3Section3_F11

Chapter3Section3_F11 - 91.304 Foundations of (Theoretical)...

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91.304 Foundations of (Theoretical) Computer Science Chapter 3 Lecture Notes (Section 3.3: Definition of Algorithm) David Martin dm@cs.uml.edu With modifications by Prof. Karen Daniels, Fall 2011 This work is licensed under the Creative Commons Attribution-ShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/by- 1 sa/2.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.
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Overview lgorithm ± Algorithm ² Intuitive definition ilbert’s Problems ± Hilbert s Problems ² Show how definition of algorithm was crucial to one mathematical problem ² Introduce Church-Turing Thesis ± Terminology for Describing Turing Machines ² Levels of description 2
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What’s It All About? ± Algorithm : ² steps for the computer to follow to solve a problem ² well-defined computational procedure that ansforms input into output transforms input into output ² (analysis of algorithms is studied in 91.404) 3
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Hilbert’s Problems how how definition of algorithm was crucial ± Show how definition of algorithm was crucial to one mathematical problem. ² Mathematician David Hilbert (in 1900) posed his at e at c a a d be t ( 900) posed s famous grand-challenge list of 23 problems to the mathematical community. 0 th roblem: devise a “process” that tests ± 10 problem: devise a process that tests whether a given polynomial has an integral root. ² Root is assignment of values to variables such that sult = 0. result 0. ³ Example (single variable with integer coefficients): hat re the root(s)? Are they integers?
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This note was uploaded on 02/13/2012 for the course CS 91.304 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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Chapter3Section3_F11 - 91.304 Foundations of (Theoretical)...

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