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CS 381
Final Exam
Wednesday Dec 14
Fall 2005
Closed book
Philips 101 79:30pm
All problems should be straight forward. Partial credit will depend on clarity and
conciseness of your answer.
Please do not put down correct but irrelevant information.
1.
Construct a finite automaton for the set of all strings of 0’s and 1’s with an even
number of zeros and an odd number of ones.
You can draw the state diagram of the finite
automaton or you can specify the delta function by a table.
In either case you must
indicate the start state and the set of final states.
2.
Give a one or two sentence definition of the symbol
k
ij
R
which was used in converting
a finite automaton to a regular expression.
3.
Let L=
{ }
2
1
n
n
ab
n
≥
.
Prove or disprove that L is a contextfree language.
4.
Let L=
{ }
nnn
abc
abc n
+++
−≥
.
Either give a contextfree grammar for L or use the
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 Fall '07
 HOPCROFT

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