1 answer

1)Convert the following context free grammar to Chomsky Normal Form S → a X | Yb...

Question:

1)Convert the following context free grammar to Chomsky Normal Form

S → a X | Yb

X → S | λ

Y → b Y | λ

2)Some languages distinguish between uppercase and lowercase in identifiers. What are the pros and cons of this design decision?

3)Use the pumping lemma to prove that the following languages are not regular.     (The alphabet is Σ = {a, b}.)

a) L = {an b1 ak: k >= n+ l}

b) L = {ww: w ∈ Σ *}

c) L= {ak2} // this is k square

d) L ={uwwrv :u,v,w ∈ Σ+, |u| >= |v|}


Answers

1)Convert the following context free grammar to Chomsky Normal Form

S → a X | Yb
X → S | λ
Y → b Y | λ

-> Remove λ productions
S → a X | Yb | a | b
X → S
Y → b Y | b

-> Remove unit productions
S → a S | Yb | a | b
Y → b Y | b

-> Replace all productions with non-terminals except for unit productions
Below is the final CNF grammar

S → AS | YB | a | b
Y → BY | b
A → a
B → b

Note: One question at a time please -- HOMEWORKLIB RULES

.

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