# How do i determine when I am at the left most character of a turing machine tape?

I am currently making a 2 tape turing machine for a language that has a binary palindrome (ex: L = {x is over {0,1} | x is a palindrome }. I can assume that the tape is only infinite in one way (the right side). and when using 2 tapes, the first one contains the input, the other is empty, and both heads start at the beginning of the tape.

So, my process has been:

1. transfer all of the letters from tape1 to tape2 (ex: 0,0,R | U,0,R would keep the symbol 0 on tape1 and move it to the right while changing the empty symbol on tape2 to 0 and moving it right as well).
2. Reverse tape1's head to the start again. However, I'm not sure how to do this if the tape is not infinite on both sides. I've been stumped on this part for a while and am unsure of how to continue.
• One-way tape(s) Turing Machine are often modeled assuming that there is a special unwritable symbol at the beginning of the tape ('#') and the head is initially placed at its right. In the transition table you can specify the behavior when the heads are on the '#' (a move to the left of '#' will leave the head where it is). This is in my opinion the best way to interpret it (but all models are clearly equivalent).
– Vor
Apr 19 at 10:12

If $$M$$ ever tries to move its head to the left off the left-hand end of the tape, the head stays in the same place for that move, even though the transition function indicates L.
Here $$M$$ is the Turing Machine and L indicates moving the head to the left.