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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

We defined the rotational closure of language Ato be RC(A)={yx|xy鈭�A} . Show that the class of CFLs is closed under rotational closure

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))

Give an informal description of a pushdown automaton that recognizes the language in Exercise 2.9.
  1. Use the languages A={ambncnm,n鈮�0}and B={anbncmm,n鈮�0}together with Example 2.36 to show that the class of context-free languages is not closed under intersection.
  2. Use part (a) and DeMorgan鈥檚 law (Theorem 0.20) to show that the class of context-free languages is not closed under complementation.

Answer each part for the following context-free grammar G

R鈫�XRX|SS鈫�aTb|bTaT鈫�XTX|X|蔚X鈫�a|b

  1. What are the variables of G?
  2. What are the terminals of G?
  3. Which is the start variable of G?
  4. Give three strings in L(G).
  5. Give three strings not inL(G) .
  6. True or False: T鈬�aba.
  7. True or False: T鈬�鈭�aba.
  8. True or False:T鈬�T .
  9. True or False: T鈬�鈭�T.
  10. True or False:XXX鈬�鈭�aba .
  11. True or False: X鈬�鈭�aba
  12. True or False:role="math" localid="1660812124187" T鈬�鈭�XX.
  13. True or False: T鈬�鈭�XXX.
  14. True or False: S鈬�鈭�蔚.
  15. Give a description in English of L(G) .
See all solutions

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