This is weird but by pumping lemma, say
Let
L
be a regular language. There exists a constantn
such that for every stringw
inL
such that|w| >= n
|w| >= n
, we can breakw
in toxyz
such thatxy*z
is also inL
.
This lemma is strong because it argues for all regular languages. But what if the regular language L = a
? There is only one word ( a
) in it. How the pumping lemma works for this case?
If n = 2
then it is vacuously true that any w
in L
with |w| >= n
|w| >= n
satisfies the conclusion of the pumping lemma. No words in L
are long enough to serve as counterexamples. More generally, if L
is any finite language then L
satisfies the pumping lemma: just take n
to be greater than the length of the longest word in L
.
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