This Turing Machine can be built, correct?

Miscellaneous and Personal Stuff I Must Share
1

A Turing machine that, starting anywhere on the tape, halts if and only if there is a stroke somewhere on the tape.

There is such a machine, correct? I think I’ve designed one that accomplishes the above, but I want to make sure there’s not something I’m missing.

The one I have designed starts by creating a string “1, 0, 1” on the tape (halting of course if there was already a stroke on any of those three spaces) then using the two external strokes as guides for a process of scanning the spaces just to the left of the leftmost stroke and just to the right of the rightmost stroke. On finding a stroke, it halts. On finding a blank, it moves the relevant extreme stroke over one, then repeats the process.

(I don’t mean it scans both extremes on each pass, just that it goes back and forth between scanning one space past the left extreme, taking the appropriate action, then scanning one space past the left extreme, taking the appropriate action, and so on.)

That’d work, right?

2

Of course it would work.

3

IANA mathematician but I thought the Turing problem was to come up with a way of predicting whether any arbitrary Turning configuration would ever stop or not. I presume you can always contrive a configuration that you know will, or will never, stop.

4

Okay thanks.

5

I was just asking about the particular question of whether the machine described in the first line of the OP exists or not.

6

Why wouldn’t it work?

7

No reason that I could see.

8

Now figure out how to make it work with a 2D tape.

9

Could you do it in a basically similar fashion but with four “guide strokes” at the corners of an ever-expanding square?