MIT6_042JS10_lec07_prob

MIT6_042JS10_lec07_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science February 19 Prof. Albert R. Meyer revised February 19, 2010, 1407 minutes In-Class Problems Week 3, Fri. Problem 1. Let’s refer to a programming procedure (written in your favorite programming language —C++, or Java, or Python, . . . ) as a string procedure when it is applicable to data of type string and only returns values of type boolean . When a string procedure, P , applied to a string , s , returns True , we’ll say that P recognizes s . If R is the set of strings that P recognizes, we’ll call P a recognizer for R . (a) Describe how a recognizer would work for the set of strings containing only lower case Ro- man letter — a,b,...,z —such that each letter occurs twice in a row. For example, aaccaabbzz , is such a string, but abb , 00bb , AAbb , and a are not. (Even better, actually write a recognizer pro- cedure in your favorite programming language). A set of string s is called recognizable if there is a recognizer procedure for it. When you actually program a procedure, you have to type the program text into a computer system. This means that every procedure is described by some string of typed characters. If a string , s
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