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The general class of questions that some algorithm can answer in polynomial time is "P" or "class P". For some questions, there is no known way to find an answer quickly, but if provided with an answer, it can be verified quickly. The class of questions where an answer can be verified in polynomial time is "NP", standing for "nondeterministic ...
The word polynomial joins two diverse roots: the Greek poly, meaning "many", and the Latin nomen, or "name". It was derived from the term binomial by replacing the Latin root bi-with the Greek poly-. That is, it means a sum of many terms (many monomials). The word polynomial was first used in the 17th century. [6]
Coefficient: An expression multiplying one of the monomials of the polynomial. Root (or zero) of a polynomial : Given a polynomial p ( x ), the x values that satisfy p ( x ) = 0 are called roots (or zeroes) of the polynomial p .
For a long time, the main problem was to find the solutions of a single non-linear polynomial equation in a single unknown. The fact that a complex solution always exists is the fundamental theorem of algebra , which was proved only at the beginning of the 19th century and does not have a purely algebraic proof.
The formula resulting from transforming all clauses is at most 3 times as long as its original; that is, the length growth is polynomial. [10] 3-SAT is one of Karp's 21 NP-complete problems, and it is used as a starting point for proving that other problems are also NP-hard. [b] This is done by polynomial-time reduction from 3-SAT to the other ...
Can leaf powers and k-leaf powers be recognized in polynomial time? Can parity games be solved in polynomial time? Can the rotation distance between two binary trees be computed in polynomial time? Can graphs of bounded clique-width be recognized in polynomial time? [1] Can one find a simple closed quasigeodesic on a convex polyhedron in ...