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Chapter 2: Q9E (page 155)

Give a context-free grammar that generates the language

A={aibjkki=jorj=kwherei,j,k鈮�0}

Is your grammar ambiguous? Why or Why not?

Short Answer

Expert verified

Context-free grammar:

S鈫�TabCATbcTab鈫�aTabb蔚Tbc鈫�bTbcc蔚C鈫�Cc蔚A鈫�Aa蔚

The grammar is ambiguous, because a string can be derived in more than one way.

Step by step solution

01

Explain context-free grammar

Context-free grammar is the set of rules that are used to recognize the context-free language. The context-free grammar contains the production rules, variables, and terminals.

02

Provide example of context-free grammar

Consider the given language

A=aibjcki=jorj=kwherei,j,k鈮�0, The context-free grammar for the given language can be derived as follows:

S鈫�TabCATbcTab鈫�aTabb蔚Tbc鈫�bTbcc蔚C鈫�Cc蔚A鈫�Aa蔚

Consider the string 蔚 ; it can be derived in more than one way. By choosing the TabC , and substituting Tab by 蔚 , C by 蔚 . In other way, ATbc can be chosen, and substituting A by 蔚, Tbc by 蔚.

Therefore, the grammar is ambiguous, because a string can be derived in more than one way.

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Most popular questions from this chapter

Read the definitions of NOPREFIX ( A) and NOEXTEND (A) in Problem .

a. Show that the class of CFLs is not closed under NOPREFIX.

b. Show that the class of CFLs is not closed under NOEXTEND.

Let E={aibj|i鈮�jand2i鈮�j}. Show thatE is context-free language.

Prove the following stronger form of the pumping lemma, wherein both pieces vandy must be nonempty when the stringS is broken up.

If Ais a context-free language, then there is a number k where, if s is any string inA of length at leastk , then s may be divided into five pieces,role="math" localid="1659706026393" s=uvxyz , satisfying the conditions:

role="math" localid="1659706054658" a.foreachi鈮�0,uvixyiz鈭�A,b.v鈮�蔚andy鈮�蔚,andc.|vxy|鈮�k,

Let G=(V,危,R,S)be the following grammar. V={S,T,U};危={0,#};R is the set of rules:

S鈫�TT|UT鈫�0T|T0|#U鈫�0U00|#

a. DescribeL(G) in English.

b. Prove thatL(G)is not regular.

Let G be the following grammar:

S鈫�T鈭�|T鈫�TaTb|TbTa|蔚

  1. Show thatL(G)={w鈭�||w鈥塩辞苍迟补颈苍蝉鈥塭辩耻补濒鈥塶耻尘产别谤鈥塷蹿鈥�a'蝉鈥塧苍诲鈥�b's} . Use a proof by induction on the length of W.
  2. Use the DK-test to show that G is a DCFG,
  3. Describe a DPDA that recognizesL(G)
See all solutions

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