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Aug 5, 2022 at 13:43 comment added Joel David Hamkins Unfortunately, there hasn't yet been any improvement.
Aug 5, 2022 at 9:54 comment added user21820 Has there been any improvements on this for the double-sided tape?
Apr 13, 2017 at 12:58 history edited CommunityBot
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Mar 3, 2012 at 13:33 comment added Joseph O'Rourke My naive question hardly deserves such a lucid and informative answer--I am grateful! Your result (that the probability of halting in that model is zero) is, well, awesome!
Mar 3, 2012 at 11:57 vote accept Joseph O'Rourke
Mar 3, 2012 at 3:28 history edited Joel David Hamkins CC BY-SA 3.0
added 315 characters in body; added 39 characters in body
Mar 3, 2012 at 3:06 comment added Joel David Hamkins With that model, the best we know is that $13.5\%$ of programs don't halt, or more specifically, $\frac{1}{e^2}$, for the trivial reason that this is the density of programs having no transition to the halt state. This is also the best we know for the two-way infinite tape model.
Mar 3, 2012 at 3:03 comment added Benjamin Steinberg @Joel, I've heard Alexei speak of this nice result many times. I always wanted to know what happens if you assume the machine stays where it is whenever it trys to move beyond the left end of the tape. This might be different than the 2-way tape because you keep moving to the left and staying awhile before moving right.
Mar 3, 2012 at 2:51 comment added Suvrit @Joel: You don't halt! (because you're unstoppable) :-)
Mar 3, 2012 at 2:44 history answered Joel David Hamkins CC BY-SA 3.0