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Chapter 2: Q10E (page 155)

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

Short Answer

Expert verified

Answer:

Informal description of the pushdown automaton that recognizes the language A={ajbjcki=jorj=kwherei,j,k鈮�0}can be given.

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,j,k鈮�0}is as follows,

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

Therefore, the informal description has been given

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Most popular questions from this chapter

Show that F = { aibj|i=kjfor some positive integerk } is not context free

Use the pumping lemma to show that the following languages are not context free.

a. {0n1n0n1n|n鈮�0}

b.{0n#02n#03n|n鈮�0}

c. role="math" localid="1659701399563" {w#t|w鈥娾赌�is鈥娾赌�a鈥娾赌�substring鈥娾赌娾��of鈥娾赌�t,where鈥娾赌�w,t鈭�(a,b)*}

d. (t1#2#......#tk|k鈮�2,each鈥娾赌�ti鈭�{a,b}*and鈥娾赌�t=t鈥娾赌�for鈥娾赌�some鈥娾赌�i鈮�j)

Convert the following CFG into an equivalent CFG in Chomsky normal form, using the procedure given in Theorem 2.9.

A鈫�BAB|B|蔚B鈫�00|蔚

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

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.
See all solutions

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