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Unformatted text preview: Massachusetts Institute of Technology 6.042J/18.062J, Spring 11 : Mathematics for Computer Science February 26 Prof. Albert R Meyer revised Sunday 27 th February, 2011, 01:33 Problem Set 4 Due : March 4 Reading: Chapter 8 8.3 . GCDs and Unique factorization, by Monday, Feb 28 Chapter 8.4 8.6 . Arithmetic mod a prime, by Wed. Mar. 2 Chapter 8.7 . Eulers Theorem, by Fri. Mar. 4 Chapter 8.8 8.9 . The RSA cryptosystem, by Mon. Mar. 7 This pset covers Ch. 7 and Ch. 8 8.6 . Problem 1. Definition 1.1. The set, RecMatch, of strings of matching brackets, is defined recursively as follows: Base case: 2 RecMatch. Constructor case: If s;t 2 RecMatch, then [ s ] t 2 RecMatch : One precise way to determine if a string is matched is to start with 0 and read the string from left to right, adding 1 to the count for each left bracket and subtracting 1 from the count for each right bracket. For example, here are the counts for two sample strings: [ ] ] [ [ [ [ [ ] ] ] ] 0 1 0 1 0 1 2 3 4 3 2 1 0...
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This note was uploaded on 10/04/2011 for the course CSCI 101 taught by Professor Leighton during the Spring '11 term at MIT.
 Spring '11
 Leighton
 Computer Science

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