Suppose that
a) show that is a context free language
b) show that for every is also context free
CFG is a Formal Grammer is used to Generate Set of strings . It is also called as Type 2 Grammer
Syntax = G= {V,T,P,S}
Given L = anbn : n > = 0
It means for a derived string have number of a's is equal to number of b's
if n=2 then L = {a2b2} String = aabb
=> aSb here S = string(i.e Derive any number of a's and any number of b's)
=> aabb ( S-> ab)
Grammer G = { V.T,P,S}
V= { S }
T = { a,b,e} (here e = epsilon)
P : S->aSb/ab/ e
S = Sta
a) Given that L2 is a CFG
as L = { anbn}
L2 is represented as L x L = { a2n b2n } if n = 1 ,
L2 = { a2 b2 } String = aabb ( in which derived string is same as L}
if n=0 L2 string derives (Epsilon e)
Therefore L2 is also a CFG.
b) Given Lk : k > = 1
Lk = {ak bk }
as L and L2 are CFG , Lk is also be CFG
ex : if k = 2
L2 derives the string aabb . It is also CFG
Suppose that a) show that is a context free language b) show that for every is...
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