I've got a really simple question about Turning Machines.
If the very first action it takes includes rewinding the tape, will it move back past the starting point or is this a special case and will it remain at the starting point?
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It really depends on which formalism you are using. Some formalisms have a tape that is infinitely extensible in both directions, while other have a left end. Within the left end camp, there are still more subdivisions. Some people say that the machine fails or produces no output when it moves off the left end of the tape (I'm thinking of work by Hamkins and Miasnikov on halting probability), while others force a special, unrewritable marker in the leftmost tape cell (Kozen does this in his Automata and Computability textbook). These formalisms are all essentially equivalent, so most people don't make a big deal about it and just use whatever is most convenient for the application at hand.
Aubrey da Cunha
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1From what I learned in class, I attest that this is the correct answer. – Nayuki Jul 15 '11 at 19:16
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The tape in a Turing machine is infinite in both directions; it is usually assumed that everything before the beginning is filled with 0.
Ignacio Vazquez-Abrams
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You could have a Turing machine that halts when it moves past the beginning of the tape. – Gabe Mar 24 '11 at 11:42
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The tape is infinitely extensible in both directions. Wikipedia has this to say:
A tape which is divided into cells, one next to the other. Each cell contains a symbol from some finite alphabet. The alphabet contains a special blank symbol (here written as 'B') and one or more other symbols. The tape is assumed to be arbitrarily extendable to the left and to the right, i.e., the Turing machine is always supplied with as much tape as it needs for its computation.
paxdiablo
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