What's the generic-case complexity of the Halting Problem on LBAs?

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I'm familiar with Hamkins' result that the generic-case complexity of the Halting Problem is polynomial in time.



What's the analogous result for the various Linear Bounded Automata?



Edit: For those unfamiliar with generic-case complexity, here is the definition from Wikipedia. The proof of the generically-polynomial complexity of the Halting Problem can be found in this paper.



The "one sentence version" of the paper is that there exists some algorithm such that the proportion of $n$-state Turing Machines for which the Halting Problem is decidable (using that algorithm) becomes 100% as $ntoinfty$.




computer-science computational-complexity computability




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  • Can this question get some links for us ignorant to these type of things? Maybe this is a good resource? I am not sure. I think the expression "the Halting Problem is Polynomial in Time" looks a little strange without more context. Isn't the halting problem the famously undecidable problem? Maybe I am just whining. But I certainly could learn more about this question if I was given a little more context.
    – Mason
    Aug 2 at 18:32






  • 1




    Of course! Sorry about that @Mason! I'm just so used to people here seeming passive-aggressive about explaining "well-known concepts" that I assumed I shouldn't say anything. I hope what I added explains any problems!
    – Isky Mathews
    Aug 2 at 19:42










  • The halting problem for LBAs is already 100% decidable by Turing machine, and I don't see a way of perturbing the definition to get something interesting. What motivated this question?
    – realdonaldtrump
    Aug 3 at 9:47










  • I wanted to know whether it would be quicker than polynomial for LBAs.
    – Isky Mathews
    Aug 3 at 12:06










  • @realdonaldtrump: I know that it's decidable but my point is that the Halting Problem is not just generically decidable, it's generically polynomial. I wondered if the LBA-Halting-Problem might have an even greater speedup generically.
    – Isky Mathews
    Aug 3 at 16:13














up vote
2
down vote

favorite












I'm familiar with Hamkins' result that the generic-case complexity of the Halting Problem is polynomial in time.



What's the analogous result for the various Linear Bounded Automata?



Edit: For those unfamiliar with generic-case complexity, here is the definition from Wikipedia. The proof of the generically-polynomial complexity of the Halting Problem can be found in this paper.



The "one sentence version" of the paper is that there exists some algorithm such that the proportion of $n$-state Turing Machines for which the Halting Problem is decidable (using that algorithm) becomes 100% as $ntoinfty$.




computer-science computational-complexity computability




share|cite|improve this question





















  • Can this question get some links for us ignorant to these type of things? Maybe this is a good resource? I am not sure. I think the expression "the Halting Problem is Polynomial in Time" looks a little strange without more context. Isn't the halting problem the famously undecidable problem? Maybe I am just whining. But I certainly could learn more about this question if I was given a little more context.
    – Mason
    Aug 2 at 18:32






  • 1




    Of course! Sorry about that @Mason! I'm just so used to people here seeming passive-aggressive about explaining "well-known concepts" that I assumed I shouldn't say anything. I hope what I added explains any problems!
    – Isky Mathews
    Aug 2 at 19:42










  • The halting problem for LBAs is already 100% decidable by Turing machine, and I don't see a way of perturbing the definition to get something interesting. What motivated this question?
    – realdonaldtrump
    Aug 3 at 9:47










  • I wanted to know whether it would be quicker than polynomial for LBAs.
    – Isky Mathews
    Aug 3 at 12:06










  • @realdonaldtrump: I know that it's decidable but my point is that the Halting Problem is not just generically decidable, it's generically polynomial. I wondered if the LBA-Halting-Problem might have an even greater speedup generically.
    – Isky Mathews
    Aug 3 at 16:13












up vote
2
down vote

favorite









up vote
2
down vote

favorite











I'm familiar with Hamkins' result that the generic-case complexity of the Halting Problem is polynomial in time.



What's the analogous result for the various Linear Bounded Automata?



Edit: For those unfamiliar with generic-case complexity, here is the definition from Wikipedia. The proof of the generically-polynomial complexity of the Halting Problem can be found in this paper.



The "one sentence version" of the paper is that there exists some algorithm such that the proportion of $n$-state Turing Machines for which the Halting Problem is decidable (using that algorithm) becomes 100% as $ntoinfty$.




computer-science computational-complexity computability




share|cite|improve this question













I'm familiar with Hamkins' result that the generic-case complexity of the Halting Problem is polynomial in time.



What's the analogous result for the various Linear Bounded Automata?



Edit: For those unfamiliar with generic-case complexity, here is the definition from Wikipedia. The proof of the generically-polynomial complexity of the Halting Problem can be found in this paper.



The "one sentence version" of the paper is that there exists some algorithm such that the proportion of $n$-state Turing Machines for which the Halting Problem is decidable (using that algorithm) becomes 100% as $ntoinfty$.





computer-science computational-complexity computability





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 2 at 19:40
























asked Aug 2 at 17:21









Isky Mathews

775214




775214











  • Can this question get some links for us ignorant to these type of things? Maybe this is a good resource? I am not sure. I think the expression "the Halting Problem is Polynomial in Time" looks a little strange without more context. Isn't the halting problem the famously undecidable problem? Maybe I am just whining. But I certainly could learn more about this question if I was given a little more context.
    – Mason
    Aug 2 at 18:32






  • 1




    Of course! Sorry about that @Mason! I'm just so used to people here seeming passive-aggressive about explaining "well-known concepts" that I assumed I shouldn't say anything. I hope what I added explains any problems!
    – Isky Mathews
    Aug 2 at 19:42










  • The halting problem for LBAs is already 100% decidable by Turing machine, and I don't see a way of perturbing the definition to get something interesting. What motivated this question?
    – realdonaldtrump
    Aug 3 at 9:47










  • I wanted to know whether it would be quicker than polynomial for LBAs.
    – Isky Mathews
    Aug 3 at 12:06










  • @realdonaldtrump: I know that it's decidable but my point is that the Halting Problem is not just generically decidable, it's generically polynomial. I wondered if the LBA-Halting-Problem might have an even greater speedup generically.
    – Isky Mathews
    Aug 3 at 16:13
















  • Can this question get some links for us ignorant to these type of things? Maybe this is a good resource? I am not sure. I think the expression "the Halting Problem is Polynomial in Time" looks a little strange without more context. Isn't the halting problem the famously undecidable problem? Maybe I am just whining. But I certainly could learn more about this question if I was given a little more context.
    – Mason
    Aug 2 at 18:32






  • 1




    Of course! Sorry about that @Mason! I'm just so used to people here seeming passive-aggressive about explaining "well-known concepts" that I assumed I shouldn't say anything. I hope what I added explains any problems!
    – Isky Mathews
    Aug 2 at 19:42










  • The halting problem for LBAs is already 100% decidable by Turing machine, and I don't see a way of perturbing the definition to get something interesting. What motivated this question?
    – realdonaldtrump
    Aug 3 at 9:47










  • I wanted to know whether it would be quicker than polynomial for LBAs.
    – Isky Mathews
    Aug 3 at 12:06










  • @realdonaldtrump: I know that it's decidable but my point is that the Halting Problem is not just generically decidable, it's generically polynomial. I wondered if the LBA-Halting-Problem might have an even greater speedup generically.
    – Isky Mathews
    Aug 3 at 16:13















Can this question get some links for us ignorant to these type of things? Maybe this is a good resource? I am not sure. I think the expression "the Halting Problem is Polynomial in Time" looks a little strange without more context. Isn't the halting problem the famously undecidable problem? Maybe I am just whining. But I certainly could learn more about this question if I was given a little more context.
– Mason
Aug 2 at 18:32




Can this question get some links for us ignorant to these type of things? Maybe this is a good resource? I am not sure. I think the expression "the Halting Problem is Polynomial in Time" looks a little strange without more context. Isn't the halting problem the famously undecidable problem? Maybe I am just whining. But I certainly could learn more about this question if I was given a little more context.
– Mason
Aug 2 at 18:32




1




1




Of course! Sorry about that @Mason! I'm just so used to people here seeming passive-aggressive about explaining "well-known concepts" that I assumed I shouldn't say anything. I hope what I added explains any problems!
– Isky Mathews
Aug 2 at 19:42




Of course! Sorry about that @Mason! I'm just so used to people here seeming passive-aggressive about explaining "well-known concepts" that I assumed I shouldn't say anything. I hope what I added explains any problems!
– Isky Mathews
Aug 2 at 19:42












The halting problem for LBAs is already 100% decidable by Turing machine, and I don't see a way of perturbing the definition to get something interesting. What motivated this question?
– realdonaldtrump
Aug 3 at 9:47




The halting problem for LBAs is already 100% decidable by Turing machine, and I don't see a way of perturbing the definition to get something interesting. What motivated this question?
– realdonaldtrump
Aug 3 at 9:47












I wanted to know whether it would be quicker than polynomial for LBAs.
– Isky Mathews
Aug 3 at 12:06




I wanted to know whether it would be quicker than polynomial for LBAs.
– Isky Mathews
Aug 3 at 12:06












@realdonaldtrump: I know that it's decidable but my point is that the Halting Problem is not just generically decidable, it's generically polynomial. I wondered if the LBA-Halting-Problem might have an even greater speedup generically.
– Isky Mathews
Aug 3 at 16:13




@realdonaldtrump: I know that it's decidable but my point is that the Halting Problem is not just generically decidable, it's generically polynomial. I wondered if the LBA-Halting-Problem might have an even greater speedup generically.
– Isky Mathews
Aug 3 at 16:13















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