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I think this question should be closed for two different reasons:
I. This is against the policy about not allowing questions about unpublished not-peer-reviewed approaches to open problems and crank-friendly topics. The OP states that this is equivalent to "$\mathbf{P}$ vs. $\mathbf{NP}$", and therefore it falls under that policy and should be closed as off-topic. The cosmetics like the way of phrasing the question are irrelevant. In fact some users on Math.SE have advised the OP to phrase the question in that way to get around our policy, see here:
If you cross-post this question to CSTheory, it may not be well-received. If you re-phrase your question to something like "Are there known barriers to this approach to P \neq NP?", this might be better.
II. The post is also not a real question, refer to the comments by OP under the Math.SE post:
"I am no researcher and therefore I am only privately interested in this question"
"With my above question, I wanted only to share my main idea for attacking this problem. Perhaps some experienced mathematician like you is able to use my idea in some way."
The OP who states that she/he is not a expert wants to share his idea about how to solve the open problem with experts, this is clearly not-a-real-question.
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$\begingroup$ @Lev Reyzin, I agree and will not argue about the fact that an idea (by a non-expert in this case) can be enlightening for others (including experts), but csthoery is not an idea sharing place AFAIK. The effects of permitting people posting their ideas on how to solve (crank-friendly) open problems are similar. (This already happens on theory mailing lists and news groups which have been overrun by non-experts and there you can find way more ideas than you would like to see.) $\endgroup$– KavehFeb 28, 2011 at 2:43
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4$\begingroup$ I am not 100% sure how I feel about this myself, but Would you say any question that basically goes "Here's an idea for how to resolve P vs NP. Are there any known reasons why it should fail?" is off-topic? $\endgroup$– Lev Reyzin ModFeb 28, 2011 at 4:06
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1$\begingroup$ @Lev, I think we should separate two things here. About this question, the honest post would be: "I am a non-expert, I come up with this idea/approach about solving the open problem P vs NP and I want to share it with experts", and that would be clearly off-topic and not-a-real-question. $\endgroup$– KavehFeb 28, 2011 at 10:03
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2$\begingroup$ @Lev, About the general question, I think sharing ideas about how to solve open problems is a good thing, but csthoery is not the place for it, as it is not a place for discussions. I can imagine a honest real question related to P vs NP that can be answered, but so far, AFAIR, all of such questions were veiled attempts to circulate the policy. A serious research level question about a proposed approach to an open problem asking if the approach can work or is useful to study is off-topic IMHO, clearly when it is by a non-expert, because there is not a definite answer, $\endgroup$– KavehFeb 28, 2011 at 10:10
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$\begingroup$ [continued] they are skipping the step to submit a draft to arXiv and then asking if experts think that their approach can work, but it is essentially the same thing. The fact that the OP has not submitted a draft to arXiv does not change the situation IMHO. I share the eagerness to see a solution to the problem, but there are other places (mailing lists, news groups, arXiv) for this kind of stuff and they have overrun by non-experts, and I don't want to see the same thing happening here. Experts will probably put their serious approaches and ideas to solve an open problem in an article, $\endgroup$– KavehFeb 28, 2011 at 10:15
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$\begingroup$ [continued] and post it on arXiv or ECCC or their webpage, and after peer-review they would be published in conferences or journals, e.g. Mulmuley's GCT program. (I personally would be happy to see a TCS forum where people would discuss the possible approaches and share their ideas, but I don't think cstheory is the right place for them. If there is enough interest, we can set up such a forum, it should not be very difficult, and technical staff in departments or institutes like IAS should be capable of setting up some open source software for this purpose.) $\endgroup$– KavehFeb 28, 2011 at 10:22
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$\begingroup$ But I think the question you mentioned can be OK if it is asking about what is known and that may be fine IMO, i.e. the question is about a known approach and what is known about it, it is not a new approach that OP just come up with. (I would be happy with new approaches also if they are by experts but I don't see any reasonable way of restrict asking such questions on cstheory to experts.) $\endgroup$– KavehFeb 28, 2011 at 10:26
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1$\begingroup$ @Kaveh: “If there is enough interest, we can set-up such a forum, it should be very difficult”: I am not sure, but this sounds contradictory to the latter part. Perhaps did you mean to say that it should not be very difficult? $\endgroup$ Feb 28, 2011 at 10:29
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2$\begingroup$ I see your point and you might be right. I think that especially if we keep getting these types of questions it might be a good idea to start closing them. But questions should be judged on their own merit, regardless of who is asking. $\endgroup$– Lev Reyzin ModFeb 28, 2011 at 16:19
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$\begingroup$ I can not see the harm in stating an idea and asking specific questions related to it (research-level assumed). The question discussed here is not the best specimen, though. $\endgroup$– RaphaelFeb 28, 2011 at 18:20
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2$\begingroup$ @Kaveh: About the comment edit yesterday: there is nothing wrong with your edit, but please keep in mind that editing a comment after the five-minute edit window is a moderator privilege. In general, moderators are expected to use their privilege only when it is necessary. (I wondered whether I should say this or not at that time, but I have decided to say this.) $\endgroup$ Mar 1, 2011 at 23:53
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1$\begingroup$ @Tsuyoshi, thanks, I was also wondering if it is right thing to do, I understand that it is a moderator privilege by system but I think it should be possible for others to do the same thing (do you know why SE imposes this restriction?). What I was doing before noticing that I can edit comments after the 5 min window was deleting the comment and reposting the corrected version (which seemed to cause more confusion). I make too many mistakes/typos when writing quickly and thought that it would be OK to fix them. I will be more careful about editing comments after 5 min window. $\endgroup$– KavehMar 2, 2011 at 1:25
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$\begingroup$ [continued] ps: this sometimes happens unintentionally also since the system does not give any warnings about using mod powers and if I haven't refreshed the page I don't see the amount of time that has passed. I would be nice if I had two separate accounts, one as a normal user and one for mod purposes. pss: I think it is good that you have decided to say it, it is good to get feedback about what I do wrong as mod, and would be happy to hear similar criticisms in future if you notice I am misusing the mod powers in any way. Thank you. :) $\endgroup$– KavehMar 2, 2011 at 1:27
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2$\begingroup$ The reason you're not allowed to edit comments after five minutes is that the discussions become impossible to follow (this can happen when people delete comments as well). I agree that five minutes is probably too short, and ten minutes would be better. $\endgroup$ Mar 2, 2011 at 21:45