Talk:Probabilistically checkable proof

message: The following was written:
PCP[r(n), q(n)] ⊆ NTIME(2^(r(n))q(n)+poly(n)), if the verifier is constrained to be non-adaptive.
I believe that the requirement of the verifier being non-adaptive is not necessary. Think of a non-deterministic machine that  guesses all necessary bits from the proof pi. However, the machine needs to remember the accessed bits of pi to check for consistence. Otherwise, the verifier might accept inputs x that are not in the set. All this can be done in time poly(n, 2^(r(n)q(n)). See the book of Arora and Barak on page 242 Remark 11.6.3; although, they forget to mention the check for consistency and hence the polynomial increase in the NTIME complexity.   — Preceding unsigned comment added by 91.79.59.157 (talk) 18:58, 21 March 2016 (UTC)
thread_title:  PCP(r(n),q(n)) vs NTIME 

message: This following:
If NP = PCP (o(log), o(log)) then NP = P
Is a contradiction to the statement:
NP = PCP (o(log), o(1))
:It is indeed a contradiction, because the second statement is just false. NP = PCP(O(log),O(1)) is the correct statement, which the first statement doesn't contradict. --Robin (talk) 18:32, 20 August 2009 (UTC)
thread_title:  Mistakes ? 

message: During several automated bot runs the following external link was found to be unavailable. Please check if the link is in fact down and fix or remove it in that case!
* http://www.cs.jhu.edu/~scheideler/courses/600.471_S03/lecture_8.pdf
** In PCP (complexity) on Mon Jul 17 14:21:25 2006, 403 Forbidden
** In PCP (complexity) on Thu Jul 27 00:27:08 2006, 403 Forbidden
----maru   (talk)  contribs 04:27, 27 July 2006 (UTC)
thread_title:  Dead link 

message: Maybe I'm missing something, but if NP = PCP(log, O(1)), then doesn't this imply that NP is a subset of PCP(log, poly), so it therefore can't strictly include PCP(log, poly) (By antisymmetricity of set inclustion)?
:The original editor probably meant the symbol to just mean inclusion (instead of strict inclusion). I changed it to equality. Arbor 17:10, 5 September 2006 (UTC)
thread_title:  Strict Inclusion? 

message: I see no reason why this should be merged.  Most major complexity classes have their own article, even those less imortant than PCP.  The PCP article and the PCP theorem article are long enough to stand on their own, certainly.  I suggest removing the tag unless there's some justification. CRGreathouse (t | c) 05:12, 8 October 2006 (UTC)
thread_title:  Merge? 

message: Can someone include the details of PCP and error correcting codes here in this page... that seems to be an important work but is not cited anywhere.  —Preceding unsigned comment added by 220.227.207.32 (talk) 10:39, 25 December 2008 (UTC)
thread_title:  PCP and error correcting codes 

message: As a complexity class, PCP doesn't really stand alone, because it is the same as NP. But as a subtopic in theoretical computer science, we certainly need a separate article on PCP's and the PCP theorem. Would it be a good idea to move this article to probabilistically checkable proof (current a redirect to here)? That would I think better focus the article on PCPs as a technique and less focus it on PCP as a (nonexistent) independent complexity class. —David Eppstein (talk) 21:16, 19 December 2009 (UTC)
replies: text: Is PCP even used as a complexity class without specifying randomness and queries? I've always seen stuff like PCP(log,O(1)), PCP(0, poly), etc. I would say that the PCP theorem asserts that NP = PCP(log, O(1)), rather than NP = PCP. --Robin (talk) 21:39, 19 December 2009 (UTC)

text: And to answer the original question, yes I agree that this article can be renamed so that it is about probabilistically checkable proofs in general. Then the article can mention the variety of classes you get from PCP(r,q), ranging from P to NEXP, and the most important class PCP(log, O(1)) which equals NP. --Robin (talk) 20:33, 23 December 2009 (UTC)
replies: text: Ok, I went ahead and performed the rename. I haven't done much yet to edit the article, other than fixing the categories to match the new name, so if someone else wants to deal with that before I get around to it that would be great. —David Eppstein (talk) 21:34, 23 December 2009 (UTC)

text: I hope the article can have more text from the viewpoint in terms of proof and verification, and treating the complexity as one aspect of it. Jackzhp (talk) 11:05, 29 September 2018 (UTC)
thread_title:  Rename? 

message: I've seen two definitions of PCPs, and I don't know which is the standard one. Is the verifier constrained to use his randomness only to make the queries, or can he use the randomness while deciding whether to accept or not? --Robin (talk) 13:49, 18 June 2010 (UTC)
replies: text: do you mean the verifier tosses a coin, if it is head, then accept the statement and the proof, or if it is a tail, then reject the statement and the proof? Such a test procedure is irrelevant to the input. Jackzhp (talk) 11:08, 29 September 2018 (UTC)
thread_title:  Verifier's random bits 

message: 79.181.73.211 (talk) 21:34, 11 April 2017 (UTC)
replies: text: An oracle can represent any function from strings to binary values. Whether you interpret the binary values as describing membership of the string in a language, or whether you interpret the string as an index and the binary value as the proof bit at that index, is up to your interpretation, it is not part of the mathematics of the model. —David Eppstein (talk) 22:08, 11 April 2017 (UTC)
thread_title:  There is no such thing "oracle access to a string" - oracle access is to a languages, not strings 

message: In the properties section, we have the following text
* PCP[0, poly(n)] = NP (By the verifier-based definition of NP.)
* PCP[O(log n),O(1)] = NP (the PCP theorem)
* PCP[log n, poly(n)] = NP
This is confusing. Jackzhp (talk) 07:56, 29 September 2018 (UTC)
thread_title: The confusing 

message: The date of proof is listed as 1992, but all the inline references are 1998 publications. Googling for these papers is confusing, there might be an "unpublished" or "partially" published version in 1992 and a "very well published in ACM journal" version in 1998. Is that so? Is there a clearer source for the 1992 proof claim than the 1998 version?  — Preceding unsigned comment added by 2800:2160:4400:170:C252:5FCD:FD06:EB11 (talk) 02:07, 25 June 2021 (UTC)
thread_title: Date of proof?