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cs381-fall02-prelim1-solutions

cs381-fall02-prelim1-solutions - CS381 Fall 2002 First Mid...

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CS381 First Mid Term Monday Oct 7, 2002 Fall 2002 Olin 155 9:05-9;55 This is a 50 minute in class closed book exam. All questions are straight forward and you should have no trouble doing them. Please show all work and write legibly. Thank you. 1. Write a regular expression for the set of all strings of 0’s and 1’s such that the number of occurrences of the substring 01 is even. Zero occurrences is even. Argue in English that your regular expression is correct. 1*(0* (01)1*0*(01)1*)*0*, or more concisely, 1*(0 + 1 + 0 + 1 + )*0*. Note that, in this expression, all occurrences of the substring 01 come from within the inner expression, 0 + 1 + 0 + 1 + , since repeating this expression, or preceeding it by a string of 1’s, or following it by a string of 0’s does not create any additional occurrences of 01. Furthermore, this inner expression contains exactly 2 occurrences of 01. Starring this expression allows any even number and only even numbers of occurrences of 01 to appear. Finally, we allow all possible strings not containing the substring 01, i.e. 1*0*,
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