(5 pt.) Describe the error in the following proof that ? = ?∗?∗ is not a...
-
(5 pt.) Describe the error in the following proof that ? = ?∗?∗ is not a regular language.
Proof (by contradiction). Assume that ? is regular. Let ? be the pumping length for ? given by the pumping lemma. Choose string ? = 0?1?. ? is a valid string because ? ∈ ? and |?| > ?. In class, we showed that ? cannot be pumped (see Example 1 in slides 12-16 of Lecture Slides 08). This is a contradiction. Therefore, ? is not regular.
Homework Answers
Solution:----------
The error is in the statement w can not be pumped, since any xyyz
will have more 0s than 1s.
The chosen string 0p1p has equal numbers of
0s and 1s and is in the language.
If pumped then it loses the equal number of 0 and 1 property, but
the resulting string is in the language C because it still has all
0s before 1s.
We need to find a string that can not be pumped in order
to show C is not regular.
Add Answer to:
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