Homework_3 - Theory of Computing CS 3810, Fall 2009...

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Theory of Computing Homework 3 CS 3810, Fall 2009 Due Friday, September 18 Each problem should be submitted on a separate piece of paper. Please put your netid on your homework! 1. Describe the set { } { } { } { } 22 010 1| 1 * 0*1 01010 1| nn εε ≥+ I . Why did we add the term { } ε + to the two subexpressions? 2. a) Write a regular expression for all strings of 0’s and 1’s having an even number of 0’s. Does every string denoted by your expression have an even number of 0’s? Is every string with an even number of 0’s included in your regular expression? b) Write a regular expression for all strings of 0’s and 1’s in which all 0’s occur before any 1’s. c) Write a regular expression for all strings of 0’s and 1’s that are of odd length. 3. a) Write a regular expression for all strings of 0’s and 1’s in which the total number of zeros to the right of each 1 is even. b) Write a regular expression for all strings of 0’s and 1’s in which at least one copy of the substring 01 occurs before any copy of the substring 10 occurs in the string.
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Homework_3 - Theory of Computing CS 3810, Fall 2009...

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