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Chapter 2: 14E (page 156)

Question: Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.

A鈫�BAB|B|蔚B鈫�00|蔚

Short Answer

Expert verified

S鈫�BD|BB|AB|CC|BA|蔚A鈫�BD|BB|AB|CC|BAB|CCC|0D鈫�AB

Step by step solution

01

Define Chomsky Normal Form (CNF)

In theory of computation, context free grammar (CFG) generates the possible strings in a language. CFG is in Chomsky normal form (CNF) if the production rules in it are of the following forms:

A鈫�BC

A鈫�a

02

Add a new start symbol S

S鈫�A

A鈫�BAB | B | 蔚

B鈫�00 | 蔚

03

Step 3: Remove ε-productions.

A 鈫�蔚

B鈫�蔚Remove,A鈫�蔚S鈫�A|蔚A鈫�BAB|BB|BBR00|蔚RemoveB鈫�蔚S鈫�A|蔚

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Most popular questions from this chapter

Let B=aibjcki,j,k鈮�0andi=jori=k. Prove that B is not a DCFL.

Give an informal description of a pushdown automaton that recognizes the language in Exercise 2.9.

Consider the following CFG:

S鈫�SS|TT鈫�aTb|ab

Describe L(G)and show that G is ambiguous. Give an unambiguous grammar(H) where L(H)=L(G)and sketch a proof that (H)is unambiguous.

Say that a language is prefix-closed if all prefixes of every string in the language are also in the language. Let C be an infinite, prefix-closed, context-free language. Show that C contains an infinite regular subset.

Give an example of a language that is not context free but that acts like a CFL in the pumping lemma. Prove that your example works. (See the analogous example for regular languages in Problem 1.54.)
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