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P versus NP problem

P versus NP problem
Diagram of complexity classes provided that P≠NP. The existence of problems within NP but outside both P and NP-complete, under that assumption, was established by Ladner's theorem.[1] The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. It was essentially first mentioned in a 1956 letter written by Kurt Gödel to John von Neumann. Gödel asked whether a certain NP complete problem could be solved in quadratic or linear time.[2] The precise statement of the P=NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures"[3] and is considered by many to be the most important open problem in the field.[4] It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$1,000,000 prize for the first correct solution. Context[edit]

Related:  ComputationalAIMachine learning/nlp/AI

Computational complexity theory Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Non-Human Consciousness Exists Say Experts. Now What? Non-Human Consciousness Exists Say Experts. Now What? Phillip Low at Singularity University Have you ever considered the consciousness, or unconsciousness, of your dog? Well, a group of neuroscientists have been thinking on the subject pretty seriously, and it was announced last week that "humans are not the only conscious beings in the universe". Earlier this month, some of the leading scientists from around the world congregated at the Hotel Du Vin in Cambridge to discuss the evidence that has amassed over the years. NP - Wikipedia From Wikipedia, the free encyclopedia NP may refer to: Arts and entertainment[edit] Organizations[edit] Mike Alder Mike Alder is an Australian mathematician and philosopher who was an Assistant Professor at the University of Western Australia . [ 1 ] Alder is known for his popular writing, such as sardonic articles about the lack of basic arithmetic skills in young adults. [ 2 ] Newton's flaming laser sword [ edit ] Newton's flaming laser sword is a philosophical razor devised by Alder in an essay ( Newton's Flaming Laser Sword or: Why mathematicians and scientists don't like philosophy but do it anyway ) on the conflicting positions of scientists and philosophers on epistemology and knowledge . It was published in Philosophy Now in May/June 2004. The razor is humorously named after Isaac Newton , as it is inspired by Newtonian thought , and is "much sharper and more dangerous than Occam's Razor ". [ 3 ] Title: The Mystery of the Binary Author: Viznut Originally published in the [ALT] magazine issue 0x0000 The subcultures of computing are very young. There are no legends nor values that come from the distant past. No ancient mysticism, no generations-old symbols that have deep emotional effects. Automated Grading Software In Development To Score Essays As Accurately As Humans Roboreaders that can score essays in standardized tests could also help teachers grade and students becomes better writers. April 30 marks the deadline for a contest challenging software developers to create an automated scorer of student essays, otherwise known as a roboreader, that performs as good as a human expert grader. In January, the Hewlett Foundation of Hewlett-Packard fame introduced the Automated Student Assessment Prize (ASAP…get it?)

NP-hardness - Wikipedia Definition[edit] A decision problem H is NP-hard when for every problem L in NP, there is a polynomial-time reduction from L to H[1]:80 An equivalent definition is to require that every problem L in NP can be solved in polynomial time by an oracle machine with an oracle for H.[7] Informally, we can think of an algorithm that can call such an oracle machine as a subroutine for solving H, and solves L in polynomial time, if the subroutine call takes only one step to compute. Another definition is to require that there is a polynomial-time reduction from an NP-complete problem G to H.[1]:91 As any problem L in NP reduces in polynomial time to G, L reduces in turn to H in polynomial time so this new definition implies the previous one.

Dunning–Kruger effect The Dunning–Kruger effect is a cognitive bias in which low-ability individuals suffer from illusory superiority, mistakenly assessing their ability as much higher than it really is. Psychologists David Dunning and Justin Kruger attributed this bias to a metacognitive incapacity, on the part of those with low ability, to recognize their ineptitude and evaluate their competence accurately. Their research also suggests corollaries: high-ability individuals may underestimate their relative competence and may erroneously assume that tasks which are easy for them are also easy for others.[1]

Combinatorial Game Theory Combinatorial Game Theory studies strategies and mathematics of two-player games of perfect knowledge such as chess or go (but often either concentrating instead on simpler games such as nim, or solving endgames and other special cases). An important distinction between this subject and classical game theory (a branch of economics) is that game players are assumed to move in sequence rather than simultanously, so there is no point in randomization or other information-hiding strategies. The bible of combinatorial game theory is Winning Ways for your Mathematical Plays, by E. R. Berlekamp, J. H.