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Chapter 0: Q25P (page 1)

Give an example of an undecidable language B, where B鈮�mB.

Short Answer

Expert verified

is an example of undecidable language.B=1,T:T鈭�H鈭�0,T:T鈭�H

Step by step solution

01

Undecidability

A problem is undecidable if no Turing Machine exist which will halt in finite amount of time.

02

Example of undecidable language

Assume H : Language of all the Turing Machine which halts on empty input. This shows H is undecidable.

Now, let us define B as:


Here, T is also a Turing Machine for some language.

If B is decidable, then a Turing Machine M for language B will show the existence of a TM M' which will decide H . Also M' with input T must run M on input (1,T) .

Also, for a TM T and y鈭�0,1we will have:

y,T鈭�B鈬�1-y,T鈭�B鈬�1-y,T鈭�B

So, B reduces to Band B is not decidable as H is not decidable because no Turing Machine exists M' to decide it as stated in starting of the solution.

Hence, B is undecidable but yet.

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