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Chapter 2: Q12E (page 129)

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

Short Answer

Expert verified

Answer

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 G,

R鈫�XRX|SS鈫�aTb|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 G.

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Most popular questions from this chapter

Let D={xy|x,y鈭�{0,1}*and|x|=|y|butx鈮�y}.X1,鈥�,XnShow thatD is a context-free language.

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

Give informal descriptions and state diagrams of pushdown automata for the languages in Exercise 2.4

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.

For string W and t , write if the symbols of W are a permutation of the symbols of t . In other word,w鈮�t if t and W have the same symbols in the same quantities, but possibly in a different order.

For any string W , defines SCRAMBLE(w)={t|t鈮�w}. For any language A, let .SCRAMBLE(A)={t|t鈭�SCRAMBLE(w)鈥塮辞谤鈥塻辞尘别鈥�w鈭�A}

  1. Show that if鈭�={0,1} , then the SCRAMBLEof a regular language is context free.
  2. What happens in part (a) if鈭� contains three or more symbols? Prove your answer.
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