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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→XRX|SSaTb|btaT→XTX|X|εX→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 B be the language of all palindromes over {0,1} containing equal numbers of 0s and 1s. Show that B is not context free.

For any language, let SUFFIX() ={v|uv∈Aforsomestringu}. Show that the class of context-free languages is closed under the SUFFIX operation

Convert the CFG given in Exercise 2.1 to an equivalent PDA, using the procedure given in Theorem 2.20

Answer each part for the following context-free grammar G

R→XRX|SS→aTb|bTaT→XTX|X|εX→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⇒aba.
  7. True or False: T⇒∗aba.
  8. True or False:T⇒T .
  9. True or False: T⇒∗T.
  10. True or False:XXX⇒∗aba .
  11. True or False: X⇒∗aba
  12. True or False:role="math" localid="1660812124187" T⇒∗XX.
  13. True or False: T⇒∗XXX.
  14. True or False: S⇒∗ε.
  15. Give a description in English of L(G) .

Let G be the following grammar:

S→T−|T→TaTb|TbTa|ε

  1. Show thatL(G)={w−||w contains equal number of a's and 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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