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Tractable problems are those which can be solved in polynomial cost, while intractable problems are those which can only be solved in an exponential cost (the former solutions are commonly regarded as efficient although an exponential-time algorithm could turn out to be more efficient than a polynomial-time algorithm for some range of input sizes).

Quantum Computing Hagar, Amit 2007

Proofs about what polynomial-time Turing machines can do will be applicable to any polynomial-time Turing machines, regardless of what the laws of physics happen to be.

Humankind’s Basic Picture of the Universe Sean 2006

Cook discusses his move to the University of Toronto in 1970 and the reception of his work on NP-completeness, leading up to his A.M. Turing Award for contributions to the theory of computational complexity, including the concept of nondeterministic, polynomial-time completeness.

Oral History Interview with Stephen Cook 2002

Nevertheless, even if the practicalities get in the way, the mere fact of the existence of a potential polynomial-time solution will certainly make mathematicians sit up and take notice.

Ars Technica Chris Lee 2011

For simple games without coalition structures, we then provide a characterization of the core that matches the one for the full information case, and use it to derive a polynomial-time algorithm to check core nonemptiness.

unknown title 2009

Is there a polynomial-time algorithm that outputs any reasonable compressed representation of the optimal path?

Ernie's 3D Pancakes Jeff Erickson 2009

Is there a polynomial-time algorithm that can tell whether you have done so? then it is an easy exercise to find the clique.

Gowers's Weblog 2009

Is there a polynomial-time algorithm that will tell you, with probability at least, which is the case?

Gowers's Weblog 2009

polynomial-time

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