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Here is a simple turing machine, that accepts only $0$.

tm accepts zero

For this, it read $0$, write it with $x$, then move to right and checks end, if it is end it accepts.

With that logic, I can also add this 1->x,R, then it accepts all strings of length 1, {'0','1'}.

tm accepts strings of length 1

What I want to do is, instead of writing to logic I want to write one, $anything$ -> $another_thing$,R.

Can I do it?

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A Turing machine diagram is a form of communication. Its goal is to describe a Turing machine — usually defined as a tuple with a specific format — in a form which is easier to grasp. As such, you can use whatever shortcut you want, as long as everybody understands what you mean. This might entail your explaining some non-standard notation which you invented as shorthand.

Your professor might have different ideas about this, but the answer I gave is valid for the working mathematician.

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