Timeline for Is there a physically realizable inductive turing machine that can solve Hilbert's $10$th problem and can it overcome Church-Turing Hypothesis?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 31, 2017 at 3:34 | comment | added | Turbo | thank you very much for the finer description of algorithms. That comment did help me out more. | |
| Jul 31, 2017 at 1:02 | comment | added | Joel David Hamkins | For example, the topic of 2-dce, 3-dce, n-dce, $\omega$-dce, which is the study of algorithms that are allowed to change their mind about the output a specific number of times at most, counts now as completely standard classical material. So the standard treatment of computability theory already includes a robust discussion of the functions computable-in-the-limit and far more. So everyone is on board and conversant with the actual mathematics here. What is left out are the contentious, mathematically empty claims that these concepts somehow mean that the Church-Turing thesis is refuted. | |
| Jul 30, 2017 at 2:49 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 1368 characters in body
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| Jul 29, 2017 at 19:03 | vote | accept | Turbo | ||
| Jul 29, 2017 at 19:07 | |||||
| Jul 29, 2017 at 13:39 | comment | added | Joel David Hamkins | I don't think anyone has a closed mind about the topic, and certainly the topic of computability-in-the-limit, which as far as I can tell is basically identical to the inductive TM model, is a standard part of the curriculum in computability theory and has been for decades. | |
| Jul 29, 2017 at 13:16 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Address Church-Turing issue.
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| Jul 29, 2017 at 13:10 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Address Church-Turing issue.
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| Jul 29, 2017 at 11:13 | comment | added | Turbo | Ok I will check on that but he also says these are realizable link.springer.com/chapter/10.1007/0-387-26806-5_4 and link.springer.com/chapter/10.1007/0-387-26806-5_5. So are his machines reasonable and worth studying with an open mind? Look at Martin Davis comment in wiki (he says IMs are TMs with O and not what you say). | |
| Jul 29, 2017 at 11:10 | comment | added | Joel David Hamkins | Well, I am not saying that inductive Turing machines are the same as Turing machines with an oracle for the halting problem. But I am saying that they compute the same functions. | |
| Jul 29, 2017 at 11:09 | comment | added | Turbo | Please look at article columbia.edu/itc/hs/medinfo/g6080/misc/p82-burgin.pdf in acm. | |
| Jul 29, 2017 at 11:06 | comment | added | Turbo | It solves HaltP and Hilb10 without being a TM with oracle (that is the entire hypothesis if you read his comment in blog.computationalcomplexity.org/2007/03/…). So I am still not in clear. | |
| Jul 29, 2017 at 11:05 | comment | added | Turbo | I think the entire claim of inductive turing machine is that they are non-equivalent to TMs with oracles. So from Burgin's view IMs are not same as TMs with Oracles. If you take his superrecursive algorithms book that is what it says and it is a well cited book and this is where my confusion lies. | |
| Jul 29, 2017 at 11:01 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |