Comments on: A Short Note on the Halting Problem

By: Kurt

Kurt — Tue, 29 Apr 2008 02:15:43 +0000

Not really. The matter of how the TM is implemented is separate from whether it is an LBA or not. In their paper, <>B<> is the set of TMs that 'crash' almost immediately upon starting. They deliberately choose a TM model in which nearly <>all<> machines crash almost immediately upon starting, so as a result <>B<> contains almost all TMs in that model. But it's a totally superficial result.You could, for whatever perverse reason, implement LBAs in something like their TM model, and indeed if you did that, most of them would crash almost immediately upon starting. But those would not be very interesting programs -- they wouldn't even be able to read all of their input. The interesting LBAs, that actually do some nontrivial computing, all lie outside of <>B<>.

By: abel

abel — Mon, 28 Apr 2008 23:05:50 +0000

What I wanted to say is that if I am not wrong, for each LBA, we can find an equivalent Turing Machine of the same kind as the ones used in the paper.Of course, the way I phrased it before was pretty nonsensical.

By: Kurt

Kurt — Sun, 27 Apr 2008 01:58:56 +0000

Hi Abel,I was wondering if you would find this post, since there was no way to ping back to Scott’s post.I’m not sure I understand your comment about the second set being a subset of the first, though.

By: Abel

Abel — Sun, 27 Apr 2008 00:47:06 +0000

Well, the last comment should be signed by “Abel”

By: arkar

arkar — Sun, 27 Apr 2008 00:45:00 +0000

Thank you for your response. If I am not wrong (I could easily be), the second set is actually a subset of the first one (although the result for the second one does not use densities). I wonder now about the existence of a maximum set…