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I'm doing my homework, and i have a problem with multi-tape (multi-track) Turing Machine:

We have multi-tape Turing Machine, which always before moving a head left, writes a blank symbol.

Does this machine recognise the same class of languages as standard Turing machines?

Do you have any idea how to prove it? Certainly standard Turing Machine recognise a recursively enumerable language (Typa-0 in Chomsky hierarchy).

Janek Podwysocki
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1 Answers1

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Without loss of generality we can supopose that TMs do not go further to the left than the first input symbol.

Consider the following PDA P:

  1. P simulates the TM until the first step to the left and puts the output on the stack.
  2. The TM moves to the left are done via pops from the stack.
  3. When moving to the right again, the TM reads only blanks until it reaches the first untouched input symbol. P can do this in one single step.

For steps 2 and 3 we need the following: the state and direction in which the TM exits the block of blanks (between the last non-erased input symbol on the left and the first untouched one on the right) depends on the number of blanks in this block. There are infinitely many possibilities. However, there can only be a finite class of combinations of entrance/exit states and directions. Probably this can be coded into the PDA's finite control and updated every time another blank is written.

If this is correct, these TMs only accept the class of context-free languages. But these details would have to be worked out to really prove this.

Peter Leupold
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