I came across the following question in my revision. I would like to know how to solve this and in general what are the techniques I can use to make an undecidable TM decidable by changing inputs?
Suppose that there is a Turing Machine T when, starting with an empty tape, will generate an infinite sequence of programs C1, C2 .... Let L denote this set of programs.
Note that L can be recognizable by a Turing Machine M, which, given any program C, runs T until it has an output Ci equal to C. If C is in L, M will halt and accept C; otherwise M will not halt.
Show how to modify each program Ci in L to another program Ci' such that Ci and Ci' have the same functions and the set L' of all the modified programs C1', C2', ... is decidable. Justify your answer. [Hint. Make C1', C2', ... strictly increasing in size]