Talk:P/poly

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Example

I'm trying to think of a good example of a P/poly algorithm to add to this page, but I can't think of anything nontrivial and interesting. Trivial examples include: problems in P and arbitrary unary languages. The NP in P/poly implies PH collapse result implies that there's no known P/poly algorithm for any NP-complete problem. The BPP in P/poly result implies that there is a relatively simple P/poly algorithm for primality testing, but is it simple enough to present here? The only other problems that might have one are integer factorization and graph isomorphism, but I know no result regarding whether either of these problems is in P/poly. Dcoetzee 21:40, 8 July 2007 (UTC)[reply]

Follow-up thought: it might be illustrative to show a P/poly algorithm for a problem in P if that algorithm is fundamentally different from the ordinary P algorithm, perhaps simpler, and uses the advice string in an interesting way. Dcoetzee 21:47, 8 July 2007 (UTC)[reply]

An obvious example would be to find a prime greater than a given number. 193.144.198.250 (talk) 08:36, 17 March 2014 (UTC)[reply]

Bug in the proof of Adleman's theorem

I think the proof is incorrect: Repeating M t times does NOT decrease the error probability below $1/3^{t}$ but it does decrease it to $<e^{-t/18}$ (by Chernoff bound, see BPP (complexity)). If we take $t=18n$ , we get the probability of bad R for every x less than $(2/e)^{n}<1$ . Kukolar (talk) 08:01, 10 May 2009 (UTC)[reply]

You're quite right. Fixed now. — Emil J. 16:05, 23 June 2009 (UTC)[reply]

It would be great to explain the reason for the number 48. In the current proof it is just stated and not explained. Dsemeas (talk) 18:20, 9 July 2023 (UTC)[reply]

Nonobvious inference about sparse languages

The main article states:

there is a polynomial-time Turing reduction from any language in P/poly to a sparse language.

It cites reference 8 to support this. I read reference 8, and although it mentions sparse languages, it does not make the above statement explicitly, and it's not obvious to me that it has anything to do with the above statement.

Thus, if the above statement is correct, I think some further explanation needs to be added. --2600:1702:4380:4880:89E4:4A7A:497C:3D97 (talk) 01:28, 6 July 2020 (UTC)[reply]

Huh? The sparse language is the advice function (or an encoding of it as a language). Is that not obvious? —David Eppstein (talk) 01:57, 6 July 2020 (UTC)[reply]