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Chapter 4: Q4E (page 193)

Let A蔚CFG={G|G鈥�is鈥�a鈥�CFG that generates蔚}. Show thatA蔚CFGis decidable.

Short Answer

Expert verified

It can be shown that A蔚CFGis decidable.

Step by step solution

01

Explain context-free grammar

Context-free grammar generates the context-free languages by using the production rules. The context-free grammars has the productions that has the variables and terminals.

02

Show that AεCFG is decidable

Convert the context-free grammarG into an equivalentG' CNF that is represented by the Turing machine S. Construct the Turing machineM that decides A蔚CFG.

M=''On鈥�input鈥�GwhereG is a context-free grammar.

  1. Run the Turing machine Son input G,蔚, where A蔚CFGis decided by the Turing Machine S.
  2. If Saccepts, accept.
  3. IfS rejects, reject.

Therefore, It has been shown that A蔚CFGis decidable.

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