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Chapter 2: 12E (page 156)

Convert the CFG given in Exercise 2.3 to an equivalent PDA, using the procedure given in Theorem 2.20.

Short Answer

Expert verified

The Equivalent PDA is as follows,

Step by step solution

01

Explain Pushdown Automata

Pushdown Automata is the computational model that have an stack as additional memory. Pushdown automata recognizes the regular languages and context-free languages.

02

Convert the CFG to an equivalent PDA

Consider the grammar

R鈫�XRX|SSaTb|btaT鈫�XTX|X|蔚X鈫�a|b

The grammar can be converted into the equivalent PDA as follows,

The transition functions are the production rules of the grammar, that moves to state on matching the terminal symbols. The path of Push down Automata of a string can be accepted only if the string is accepted by the grammar.

Therefore, The Equivalent PDA has been obtained for the grammar .

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Most popular questions from this chapter

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

Let G=(V,危,R,鉄�STMT鉄�)be the following grammar.

鉄�STMT鉄�鈫�鉄�ASSIGN鉄�|鉄�IF-THEN鉄�|鉄�IF-THEN-ELSE鉄�鉄�IF-THEN鉄�鈫�ifconditionthen鉄�STMT鉄�鉄�IF-THEN-ELSE鉄�鈫�ifconditionthen鉄�STMT鉄�else鉄�STMT鉄�鉄�ASSIGN鉄�鈫�a:=1

危={if,condition,then,else,a:=1}V={鉄�STMT鉄�,鉄�IF-THEN鉄�,鉄�IF-THEN-ELSE鉄�,鉄�ASSIGN鉄�}

G is a natural-looking grammar for a fragment of a programming language, but G is ambiguous.

a. Show that G is ambiguous.

b. Give a new unambiguous grammar for the same language

Show that F = { aibj|i=kjfor some positive integerk } is not context free

Let G be a CFG in Chomsky normal form that contains b variables.

Show that if G generates some string with a derivation having at least 2b

steps, L(G)is infinite.

Use the pumping lemma to show that the following languages are not context free.

a. {0n1n0n1n|n鈮�0}

b.{0n#02n#03n|n鈮�0}

c. role="math" localid="1659701399563" {w#t|w鈥娾赌�is鈥娾赌�a鈥娾赌�substring鈥娾赌娾��of鈥娾赌�t,where鈥娾赌�w,t鈭�(a,b)*}

d. (t1#2#......#tk|k鈮�2,each鈥娾赌�ti鈭�{a,b}*and鈥娾赌�t=t鈥娾赌�for鈥娾赌�some鈥娾赌�i鈮�j)
See all solutions

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