I have checked many discussions for understanding this problem.
I understand the reasoning , unfortunately there are some drawback in my understanding.
The Blank-tape halting Problem
Input: Turing Machine M
Question : Does M halt when started with a blank tape?
So this is the reduction :
The construction of Mw is as follows :
- When started on blank tape, writes w
- Then continues execution like M
What i don't undesstand is the step 2 , in my opinion if we execute M on w maybe M will loop !!!
My second question : what the blank-tape do when executed?even if the blanktape machine halt on blank tape , how can we be sure that M halt on w .i miss something here.
Thank you in advance.