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Chapter 2: 10E (page 155)

Give an informal description of a pushdown automaton that recognizes the language in Exercise 2.9.

Short Answer

Expert verified

Informal description of the pushdown automaton that recognizes the language can be given.

A={ajbjck|i=jorj=kwherei,j,k≥0}canbegiven

Step by step solution

01

Explain pushdown automaton

Pushdown Automaton write symbols on the stack and read them. Writing a new symbol pushes down all the symbols in the stack before.

02

Give an informal description of a pushdown automaton that recognizes the language A.

Informal description of the pushdown automaton that recognizes the language

A={ajbjck|i=jorj=kwherei,k≥0}isasfollows

  1. Nondeterministic, branching to step 2 or 6.
  2. Read and push a ’s.
  3. Pop a’s, and read b ’s.
  4. If stack is empty,accept.
  5. Skip a’s and c’s input.
  6. Push b’s
  7. Read c ’s.
  8. When stack is empty and c’s finish, accept.

Therefore, the informal description has been given

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Most popular questions from this chapter

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

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) .

Give a context-free grammar that generates the language

A={aibjkki=jorj=kwherei,j,k≥0}

Is your grammar ambiguous? Why or Why not?

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

Consider the following CFG:

S→SS|TT→aTb|ab

Describe L(G)and show that G is ambiguous. Give an unambiguous grammar(H) where L(H)=L(G)and sketch a proof that (H)is unambiguous.
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