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In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete. That is, it is in NP , and any problem in NP can be reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem.
The concept of NP-completeness was introduced in 1971 (see Cook–Levin theorem), though the term NP-complete was introduced later. At the 1971 STOC conference, there was a fierce debate between the computer scientists about whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine .
This theorem was proven independently by Leonid Levin in the Soviet Union, and has thus been given the name the Cook–Levin theorem. The paper also formulated the most famous problem in computer science, the P vs. NP problem. Informally, the "P vs. NP" question asks whether every optimization problem whose answers can be efficiently verified ...
Theorem. Every group has a presentation. To see this, given a group G, consider the free group F G on G. By the universal property of free groups, there exists a unique group homomorphism φ : F G → G whose restriction to G is the identity map. Let K be the kernel of this homomorphism.
A stable binary format (called a .ppt file, like all earlier binary formats) that was shared as the default in PowerPoint 97 through PowerPoint 2003 for Windows, and in PowerPoint 98 through PowerPoint 2004 for Mac (that is, in PowerPoint versions 8.0 through 11.0) was finally created.
The master theorem always yields asymptotically tight bounds to recurrences from divide and conquer algorithms that partition an input into smaller subproblems of equal sizes, solve the subproblems recursively, and then combine the subproblem solutions to give a solution to the original problem. The time for such an algorithm can be expressed ...
Theorem — For any table of nodes there is a continuous function f(x) on an interval [a, b] for which the sequence of interpolating polynomials diverges on [a,b]. [ 14 ] The proof essentially uses the lower bound estimation of the Lebesgue constant, which we defined above to be the operator norm of X n (where X n is the projection operator on ...
C2D – Roxio-WinOnCD .c2d format; DAA – PowerISO .daa format; D64 – An archive of a Commodore 64 floppy disk. DAA – DAA: Closed-format, Windows-only compressed disk image; DMG – Macintosh disk image files; DMS – a disk-archiving system native to the Amiga.