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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 A={wtwR|w,t鈭�{0,1}*and|w|=|t|}. Prove that A is not a CFL.

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

If Aand role="math" localid="1659713811445" B are languages, defineA鈰�B={xy|x鈭�Aandy鈭�Band|x|=|y|}Show that if A andBare regular languages, thenA鈰�B is a CFL.

Recall the CFG G4 that we gave in Example 2.4. For convenience, let鈥檚 rename its variables with single letters as follows.
E鈫�E+TTT鈫�T脳FFF鈫�(E)a

Give parse trees and derivations for each string.

a. a

b. a+a

c. a+a+a

d. ((a))

Let 鈭�={1,2,3,4}andC={w鈭�危*|inw, the number of 1s equals the number of 2s, and the number of 3s equals the number of 4s} Show thatCis not context free.
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