CS381
First Mid Term
Monday Oct 7, 2002
Fall 2002
Olin 155
9:059;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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 Fall '05
 HOPCROFT
 Regular expression, Nondeterministic finite state machine, Automata theory

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