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Chapter 0: Q23P (page 1)

Show that A is decidable iff A鈮�m0*1*.

Short Answer

Expert verified

A is decidable as ..

Step by step solution

01

 Introduction to Decidability

A problem is decidable if there exist a Turing Machine exist which will halt in finite amount of time.

02

Proving A as decidable

So according to the statement in question,

If Then A must be decidable language. This is because 0*1* is a decidable language.

Now we A is decidable, then we must able to construct a corresponding Turing Machine R , which will decide A .

To prove we will construct a Turing Machine T that works as:

T= on input (R , w)

  • 路 Run R on string w .
  • 路 If R accepts, output: 01

Else

If R rejects, output: 10

From above constructed TM T , we can conclude:
w鈭�A鈬�outputfromT鈭�0*1*

So we have got mapping reduction of A on 0*1*.

This implies that: A is decidable iff

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