Consider the following problem: Given a semi-infinite tape Turing Machine M, determine if there exists an input w on which M moves the tape head to the left starting from cell number 2023 (i.e., if at some point during the computation, the head moves from cell 2023 to cell 2022). Demonstrate that the language $2023_{TM}$ is undecidable.
Let $2023_{TM}$ = {$⟨M⟩$| M is a TM and there exists an input w on which M moves the tape head to the left of cell number $2023$}.
My professor said that for the consequence of an error in the definition of the exercise $2023_{TM}$ is decidable .
- I have no clue about the mistake on the definition
- The problem of “TM makes moves left or not” is already answered here so the correct why of thinking can be answered first if “TM makes reach cell number $n$ or not”?
- Somehow after stick these two problems together (I don’t know how)