Write the Regular Expressions of following languages.
1. (a+b).(a+b) corresponds to the language cfw_aa, ab, ba, bb, that is the set of strings of
length 2 over the alphabet cfw_a, b.
2. (a+b)* corresponds to the set of all strings over the alphabet cfw_a

EXERCISES
ﬁ.1. In each case, say what language is generated by the content-free grammar
with the indicated productions.
i1.
3 -> ra.5'ﬂ'_b.3bl!t
S->aSn|bSb|cr[b
SanSblenln
S—>a5cr!b3blmiblen
A+aﬂa|h.4blaiblh
{See Example 5.3.)
smsmsua
S—FSSIIJSIH
E—> SeSl

Prove that the following languages are not regular using the pumping lemma.
:1. L = {Unlmﬂn | m,n 2 0}.
Answer.
To prove that L is not a regular language, we Will use a proof by contradiction. Assume
that L is regular. Then by the Pumping Lemma for Regula

._ l.
7.28. In each case, the grammar with the given productions does not satisfy the
LL13) property. Find an equivalent LLtl) grammar by factoring and
eliminating left recursion. '.
C. S —l* 31$ 31 H)— S1Tltl't'? T —> GT'FJDIHI}
7.28. {0:}
8H51$ 51—5obX