# What is Complete: Definition and 404 Discussions

In computational complexity theory, a problem is NP-complete when:

a brute-force search algorithm can solve it, and the correctness of each solution can be verified quickly, and
the problem can be used to simulate any other problem with similar solvability.The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. Polynomial time refers to an amount of time that is considered "quick" for a deterministic algorithm to check a single solution, or for a nondeterministic Turing machine to perform the whole search. "Complete" refers to the property of being able to simulate everything in the same complexity class.
More precisely, each input to the problem should be associated with a set of solutions of polynomial length, whose validity can be tested quickly (in polynomial time), such that the output for any input is "yes" if the solution set is non-empty and "no" if it is empty. The complexity class of problems of this form is called NP, an abbreviation for "nondeterministic polynomial time". A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP. If any NP-complete problem has a polynomial time algorithm, all problems in NP do. The set of NP-complete problems is often denoted by NP-C or NPC.
Although a solution to an NP-complete problem can be verified "quickly", there is no known way to find a solution quickly. That is, the time required to solve the problem using any currently known algorithm increases rapidly as the size of the problem grows. As a consequence, determining whether it is possible to solve these problems quickly, called the P versus NP problem, is one of the fundamental unsolved problems in computer science today.
While a method for computing the solutions to NP-complete problems quickly remains undiscovered, computer scientists and programmers still frequently encounter NP-complete problems. NP-complete problems are often addressed by using heuristic methods and approximation algorithms.

View More On Wikipedia.org
1. ### Why do atoms want to complete their shells?

Hi, I have a basic knowledge of chemistry from high school days. I remember once being told that a neutral hydrogen has one electron in its shell but it wants to complete its outer shell by having two electrons, and this makes hydrogen atom to create bonds with other atoms. Likewise, a...
2. ### Searching for a single and complete resource about nuclear fuels

Hello, I am looking for a comprehensive resource (paper, book or any kind of document) that contains the most relevant properties of most nuclear fuels. To be more specific, the information i am looking for are thermophysical properties, chemical compatibility with other materials and...
3. ### Prove that ## aa_{1}, aa_{2}, ...., aa_{n} ## is also a complete set?

Proof: Suppose for the sake of contradiction that ## aa_{i}\equiv aa_{j}\pmod {n} ## for some ## i,j\in\mathbb{Z} ## such that ## 1\leq i<j\leq n ##. Then ## aa_{i}\equiv aa_{j}\pmod {n}\implies n\mid (aa_{i}-aa_{j})\implies n\mid [a(a_{i}-a_{j})] ##. Note that ## n\mid b ## if ## n\mid (ab) ##...
4. ### B Newton’s second law as one complete law

https://www.feynmanlectures.caltech.edu/I_08.html Page 9-3. It says “In these terms, we see that Newton’s second law, in saying that the force is in same direction as the acceleration,is really three laws, in the sense that the components of force in the x, y,z directions is equal to the mass...

45. ### B Complete the Square Question

How ##4(x + \frac{1}{2})^2 + 1## can be ##(2x + 1)^2 + 1##?
46. ### Complete Square + Leibniz question (2 questions)

Homework Statement 1. How did they complete the square for these equations in the picture below? What was their thought process? 2. distance/velocity = time , velocity/acceleration = time , In leibniz notation how does this cancel out? When you divide, how does it cancel out to give you a...
47. ### Complete Noise Analysis: to find the minimum detectable signal

Problem Statement: my aim is to digitalize a 10ns narrow pulse coming from a photo diode with current ranging from 10nA-70mA, as its impossible to cover this dynamic range of >60dB using a single TIA i have an option of separating it to two channels as below using two diodes ofcourse Lowest...
48. ### Complete Combustion - which hydrocarbon will consume more O2

Homework Statement one gram of each of the following gases is introduced into a 10 L container at 25 degrees C a) propane b) ethane c) methane d) pentane which gas will consume the greatest mass of oxygen upon complete combustion? The solutions says that the right answer is D. I do not know...
49. ### Finite dimensional normed vector spaces complete ?

Homework Statement Show that finite dimensional normed vector spaces are complete. Homework Equations ##E## is a finite dimensional vector space and ##N## a norm on ##E## The Attempt at a Solution If ##\{x_n\}_n## is a Cauchy sequence in ##(E,N)##, then it is bounded and each term of the...
50. ### Understanding the Relationship between Turbulence and the Reynold Number

Homework Statement why the author gave that the complete turbulenece is indpendent on the Reynold number ?Homework EquationsThe Attempt at a Solution For the turbulence to occur , the Reynold number must be higher than certain value , am i right . So , IMO , turbulenet is dependent on the...