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I have a question and I haven't been able to figure out the answer yet. I need to do the on-line simulation of a two-head tape Turing machine using single-head tape(s). I've found some online articles for the fact that one single-head tape doesn't suffice for this problem and the simulation should be done using two single-head tapes, but I haven't been able to present an accurate simulation of two-head TM using these single-head tapes. Are there any thoughts on how to do so? Thanks,

user1667199
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    http://cstheory.stackexchange.com/ might be a better place for this question. – hatchet - done with SOverflow Sep 13 '12 at 00:14
  • by single head tape do you mean you want two tapes with one head-on each right? you bestway todo that would be something along the line of `Sate H1input h2input H1output h2output H1direction h2direction nextstate` using blanks for the heads your not using if i understand you – user23012 Nov 08 '12 at 03:39
  • This question appears to be off-topic because it is about theoretical CS, which is more appropriate at cs.stackexchange.com. – templatetypedef May 22 '14 at 16:07
  • @hatchet This would be more appropriate at cs.stackexchange.com, since cstheory is for research-level CS questions. – templatetypedef May 22 '14 at 16:07

1 Answers1

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Here's one possible way to do this:

  1. Start with a multitrack Turing machine. If you haven't seen this before, this is a TM in which each tape cell is segmented into multiple different rows, each of which can hold an independent symbol. This is equivalent to a normal Turing machine because there are only finitely many possible combinations of symbols that can be stored in a tape cell, so you can build your tape alphabet to have a different symbol for each.

  2. Have the top track hold your input and have the bottom track store the locations of the tape heads (by either marking blank for "nothing," 1 for "tape head 1 is here," 2 for "tape head 2 is here," and 3 for "both tape heads are here."

  3. To simulate one step, scan across the input and find the markers. Each time you do, you can store, in your finite-state control, which symbols are under those tape heads. There are only finitely many possibilities. Then, rescan over the tape and simulate moving the tape heads as appropriate.

Hope this helps!

templatetypedef
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