tag:blogger.com,1999:blog-20067416.post500583163902437023..comments2017-10-19T18:15:15.607-04:00Comments on Recursivity: Yet Another P vs. NP ProofJeffrey Shallitnoreply@blogger.comBlogger97125tag:blogger.com,1999:blog-20067416.post-17865996392351917392017-04-27T11:49:31.347-04:002017-04-27T11:49:31.347-04:00P versus NP is considered one of the great open pr...P versus NP is considered one of the great open problems of science. This consists in knowing the answer of the following question: Is P equal to NP? This incognita was first mentioned in a letter written by John Nash to the National Security Agency in 1955. Since that date, all efforts to find a proof for this huge problem have failed. <br />I show a solution to that problem as follows:<br />Given a number x and a set S of n positive integers, MINIMUM is the problem of deciding whether x is the minimum of S. We can easily obtain an upper bound of n comparisons: find the minimum in the set and check whether the result is equal to x. Is this the best we can do? Yes, since we can obtain a lower bound of (n - 1) comparisons for the problem of determining the minimum and another obligatory comparison for checking whether that minimum is equal to x. A representation of a set S with n positive integers is a Boolean circuit C, such that C accepts the binary representation of a bit integer i if and only if i is in S. Given a positive integer x and a Boolean circuit C, we define SUCCINCT-MINIMUM as the problem of deciding whether x is the minimum bit integer which accepts C as input. For certain kind of SUCCINCT-MINIMUM instances, the input (x, C) is exponentially more succinct than the cardinality of the set S that represents C. Since we prove that SUCCINCT-MINIMUM is at least as hard as MINIMUM in order to the cardinality of S, then we could not decide every instance of SUCCINCT-MINIMUM in polynomial time. If some instance (x, C) is not in SUCCINCT-MINIMUM, then it would exist a positive integer y such that y < x and C accepts the bit integer y. Since we can evaluate whether C accepts the bit integer y in polynomial time and we have that y is polynomially bounded by x, then we can confirm SUCCINCT-MINIMUM is in coNP. If any single coNP problem cannot be solved in polynomial time, then P is not equal to coNP. Certainly, P = NP implies P = coNP because P is closed under complement, and therefore, we can conclude P is not equal to NP.<br /><br />You could read the details in the link below...<br /><br />https://hal.archives-ouvertes.fr/hal-01509423/documentFrank Vegahttps://www.blogger.com/profile/15257641208909866601noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-26019034761540239982017-04-25T14:03:19.912-04:002017-04-25T14:03:19.912-04:00Given a number x and a set S of n positive integer...Given a number x and a set S of n positive integers, MINIMUM is the problem of deciding whether x is the minimum of S. We can easily obtain an upper bound of n comparisons: find the minimum in the set and check whether the result is equal to x. Is this the best we can do? Yes, since we can obtain a lower bound of (n - 1) comparisons for the problem of determining the minimum and another obligatory comparison for checking whether that minimum is equal to x. A representation of a set S with n positive integers is a Boolean circuit C, such that C accepts the binary representation of a bit integer i if and only if i is in S. Given a positive integer x and a Boolean circuit C, we define SUCCINCT-MINIMUM as the problem of deciding whether x is the minimum bit integer which accepts C as input. For certain kind of SUCCINCT-MINIMUM instances, the input (x, C) is exponentially more succinct than the cardinality of the set S that represents C. Since we prove that SUCCINCT-MINIMUM is at least as hard as MINIMUM in order to the cardinality of S, then we could not decide every instance of SUCCINCT-MINIMUM in polynomial time. If some instance (x, C) is not in SUCCINCT-MINIMUM, then it would exist a positive integer y such that y < x and C accepts the bit integer y. Since we can evaluate whether C accepts the bit integer y in polynomial time and we have that y is polynomially bounded by x, then we can confirm SUCCINCT-MINIMUM is in coNP. If any single coNP problem cannot be solved in polynomial time, then P is not equal to coNP. Certainly, P = NP implies P = coNP because P is closed under complement, and therefore, we can conclude P is not equal to NP.<br /><br />You could read the details in:<br /><br />http://vixra.org/pdf/1704.0335v1.pdfFrank Vegahttps://www.blogger.com/profile/15257641208909866601noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-60802645144727650022016-09-19T09:16:47.639-04:002016-09-19T09:16:47.639-04:00There were no conditions about "reconsiderati...There were no conditions about "reconsideration". Read the terms of the bet. You lost. You will pay up if you have integrity.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-47979737112866556962016-09-19T08:20:03.545-04:002016-09-19T08:20:03.545-04:00You lost because the paper is being re-considered ...You lost because the paper is being re-considered again.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-13406558447192216802016-08-27T06:13:35.056-04:002016-08-27T06:13:35.056-04:00There were no conditions on our bet. First, pay t...There were no conditions on our bet. First, pay the $500. Then we'll talk.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-43662981008664531712016-08-27T04:59:52.875-04:002016-08-27T04:59:52.875-04:00Why are you silent?
Rafee Kamouna.Why are you silent?<br /><br />Rafee Kamouna.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-14040529632183534702016-08-18T23:48:21.237-04:002016-08-18T23:48:21.237-04:00I'm ready to pay you your $500 if you invite m...I'm ready to pay you your $500 if you invite me for a cup of coffee at Waterloo. I shall pay all the travel expenses.<br /><br />best,<br /><br />Rafee Kamouna.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-26733307859897815642016-06-28T19:29:23.449-04:002016-06-28T19:29:23.449-04:00All that verbiage, and still weaseling out of the ...All that verbiage, and still weaseling out of the bet! Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-20122223008599280242016-06-28T17:50:54.032-04:002016-06-28T17:50:54.032-04:00It seems that you are in a financial crisis and yo...It seems that you are in a financial crisis and you don't care about your own research.<br /><br />I'm ready to confront you (as well as anyone) on the BBC.<br /><br />Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-3786139477895773652016-06-28T15:39:49.164-04:002016-06-28T15:39:49.164-04:00Too bad, because I expect you to pay if you wish t...Too bad, because I expect you to pay if you wish to be considered as an honorable person.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-8145230348568009862016-06-28T14:56:34.341-04:002016-06-28T14:56:34.341-04:00No, at all. Please answer the above questions and/...No, at all. Please answer the above questions and/or invite colleagues for that.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-6189399562674404752016-06-28T13:27:30.253-04:002016-06-28T13:27:30.253-04:00Why is it funny? If you had won the bet, you woul...Why is it funny? If you had won the bet, you would have expected me to pay, right?Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-74420348308632024552016-06-28T11:14:31.864-04:002016-06-28T11:14:31.864-04:00You're funny!You're funny!Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-53737777638130626102016-06-28T09:31:49.200-04:002016-06-28T09:31:49.200-04:00First pay me what you owe me.First pay me what you owe me.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-40639169232002641872016-06-28T09:04:36.285-04:002016-06-28T09:04:36.285-04:00Cook-Levin states that for every string w in any l...Cook-Levin states that for every string w in any language L in NP, a SAT formula is derived.<br /><br />Tell me what happens if the string w represents a paradox.<br /><br />This is the question that is BANNED by many complexity theorists.<br /><br />On the other hand, is paradox recognition possible or impossible?<br /><br />This is the question that is BANNED by many computability theorists.<br /><br /><br />Please address these questions and be serious, nt funny.<br /><br /><br />Rafee.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-23579455904462806732016-06-28T06:38:58.786-04:002016-06-28T06:38:58.786-04:00So, you engaged in wagering which is against your ...So, you engaged in wagering which is against your religion, and you agreed to a bet without conditions, which you then proceeded to lose, but refused to pay. Did I summarize the situation correctly?Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-81307628137828962462016-06-28T06:11:38.193-04:002016-06-28T06:11:38.193-04:00That was on the assumption of a sound technical di...That was on the assumption of a sound technical discussion which never happened.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-71908339071279001532016-06-27T17:33:32.872-04:002016-06-27T17:33:32.872-04:00You agreed to the wager above, when you said "...You agreed to the wager above, when you said "I do agree" in your comment of August 17, 2013.<br /><br />Were you lying then?<br /><br />And are you really unable to do a text search on the page to find the words "I do agree"?Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-60527376154782606372016-06-27T17:08:12.737-04:002016-06-27T17:08:12.737-04:00agree about what?
Rafee.agree about what?<br /><br />Rafee.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-77574393945124946222016-06-27T16:50:27.723-04:002016-06-27T16:50:27.723-04:00So when you said "I do agree" above you ...So when you said "I do agree" above you were lying?Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-31770332183834297092016-06-27T14:16:38.447-04:002016-06-27T14:16:38.447-04:00I never bet. It is a sort of gambling. Yes, I offe...I never bet. It is a sort of gambling. Yes, I offered a prize of one million dollar for whoever will refute Bi-Polarism Thery with its both sides:"Computer Science & Physics".<br /><br />The relationship between syntax & semantics is Fuzzy Logic Programming is the same as between space & time in General Relativity.<br /><br />The prize was declared at topcoder.com, thousands there know very well about it.<br /><br />Eight years passed with failure to refute any claim; the prize was cancelled.<br /><br /><br />best,<br /><br />Rafee Kamouna. Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-3865889266147743622016-06-27T13:26:35.450-04:002016-06-27T13:26:35.450-04:00So then why did you bet?So then why did you bet?Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-82309315705532039072016-06-27T11:32:46.482-04:002016-06-27T11:32:46.482-04:00You may not bet in Islam. Please re-check with oth...You may not bet in Islam. Please re-check with others.<br /><br />It is among non-allowable financial transactions.<br /><br />Best,<br /><br />Rafee Kamouna.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-18203620061279349422016-06-27T11:06:47.662-04:002016-06-27T11:06:47.662-04:00Rafee, what do you call a person who makes a bet, ...Rafee, what do you call a person who makes a bet, loses, and refuses to pay in your native language?Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-63403662389543951182016-06-27T10:35:46.344-04:002016-06-27T10:35:46.344-04:00Since you have no any technical comment, so you ar...Since you have no any technical comment, so you are not serious. Below is the (funny) review of another journal: They ask me for a proof of ALL mathematical problems; both in the affirmative and the negative.<br /><br />===============================<br />Reviewers' comments:<br /><br />There is no merit to this paper.<br />The author claims to have proved mathematics is inconsistent.<br />In particular the author claims to have proved SAT is NOT NP-complete.<br />Then the author has also proved NP is = P.<br />(In fact if, as the author claims to have proved, that<br />mathematics is inconsistent, then the author can prove everything,<br />including all the Millennium problems like the Riemann Hypothesis (and their negations!))<br /><br />Hence, among other things, the author claims to have a provable<br />P-time algorithm for factoring. To take the claimed proof seriously,<br />the author should first produce some factorizations of the RSA challenge<br />problems that are available on line.<br />https://en.wikipedia.org/wiki/RSA_Factoring_Challenge<br /><br />Unless and until correct answers are obtained, no referee effort should<br />be wasted in helping the author to find the mistakes in the paper.<br /><br /><br />The paper should be rejected.<br /><br />===============================================<br /><br />best,<br /><br />Rafee Kamouna.Rafee Kamounahttps://www.blogger.com/profile/12584274746853342694noreply@blogger.com