Complexity classes

NP-easy

In complexity theory, the complexity class NP-easy is the set of function problems that are solvable in polynomial time by a deterministic Turing machine with an oracle for some decision problem in NP. In other words, a problem X is NP-easy if and only if there exists some problem Y in NP such that X is polynomial-time Turing reducible to Y. This means that given an oracle for Y, there exists an algorithm that solves X in polynomial time (possibly by repeatedly using that oracle). NP-easy is another name for FPNP (see the function problem article) or for FΔ2P (see the polynomial hierarchy article). An example of an NP-easy problem is the problem of sorting a list of strings. The decision problem "is string A greater than string B" is in NP. There are algorithms such as quicksort that can sort the list using only a polynomial number of calls to the comparison routine, plus a polynomial amount of additional work. Therefore, sorting is NP-easy. There are also more difficult problems that are NP-easy. See NP-equivalent for an example. The definition of NP-easy uses a Turing reduction rather than a many-one reduction because the answers to problem Y are only TRUE or FALSE, but the answers to problem X can be more general. Therefore, there is no general way to translate an instance of X to an instance of Y with the same answer. (Wikipedia).

Video thumbnail

NP-Completeness - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Video thumbnail

SAT is NP-Hard - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Video thumbnail

NP-Hard - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Video thumbnail

Mod-01 Lec-21 Vector and Matrix Norms

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

Video thumbnail

!!Con 2016 - My favorite NP-complete problem! By Mark Dominus

My favorite NP-complete problem! By Mark Dominus NP-complete problems are the hardest problems whose solutions can be efficiently checked for correctness. An efficient method of solving any NP-complete problem would translate directly into efficient solutions for all of them. Many famous

From playlist !!Con 2016

Video thumbnail

[Calculus] Parametric Equations || Lecture 38

Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any que

From playlist Calculus 1

Video thumbnail

Exact Differential Equations Introduction Part 2

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Part 2, in class , not great quality sorry. Hope this helps.

From playlist Differential Equations

Video thumbnail

The Hardest Integral I've Ever Done

I'm not joking, this is one of those hard integral problems. It's time to tackle one of the hardest integral ever - that I've computed at least :) I hope you're enjoying these hard integral questions and hard integral problems with solutions! Some of the links below are affiliate links.

From playlist Integrals, Integrals, Integrals

Video thumbnail

Math tutorial for solving rational equations

👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa

From playlist How to Solve Rational Equations with an Integer

Video thumbnail

P vs. NP - An Introduction

P vs. NP is one of the greatest unsolved problems. Just what is it, and why is it so important? Created by: Cory Chang Produced by: Vivian Liu Script Editor: Justin Chen, Brandon Chen, Elaine Chang, Zachary Greenberg Twitter: https://twitter.com/UBehavior — Extra Resources: hackerdashe

From playlist P vs NP

Video thumbnail

P vs. NP by Sammy Mehra

Introduction to the most famous unsolved problem in Computer Science. Introduction to Turing Machines, runtime of algorithms, and the classes P and NP. What would the universe look like if P=NP. History of the problem, and attempts to solve the problem. Example adapted from https://en.wiki

From playlist CS50 Seminars 2016

Video thumbnail

P=NP?

This lecture is an informal introduction to the P=NP question in computer science: are nondeterministic polynomial time problems (NP) the same as polynomial time problems (P)? We describe what these terms mean, give a brief history, and examine some of the arguments for and against this qu

From playlist Math talks

Video thumbnail

P vs. NP and the Computational Complexity Zoo

Hackerdashery #2 Inspired by the Complexity Zoo wiki: https://complexityzoo.uwaterloo.ca/Complexity_Zoo For more advanced reading, I highly recommend Scott Aaronson's blog, Shtetl-Optimized: http://www.scottaaronson.com/blog/ ----- Retro-fabulous, cabinet-sized computers: System/360:

From playlist Interesting Videos

Video thumbnail

NP Completeness III - More Reductions - Lecutre 17

All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c

From playlist ArsDigita Algorithms by Shai Simonson

Video thumbnail

NP-Complete Explained (Cook-Levin Theorem)

What makes a problem "harder" than another problem? How can we say a problem is the hardest in a complexity class? In this video, we provide a proof sketch of the Cook-Levin theorem, introducing a critical concept known as NP-completeness. Created by: Cory Chang Produced by: Vivian Liu Sc

From playlist P vs NP

Video thumbnail

19. Complexity

MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Erik Demaine View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This lecture discusses computational complexity and introduces termi

From playlist MIT 6.006 Introduction to Algorithms, Spring 2020

Video thumbnail

Lecture 23: Computational Complexity

MIT 6.006 Introduction to Algorithms, Fall 2011 View the complete course: http://ocw.mit.edu/6-006F11 Instructor: Erik Demaine License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.006 Introduction to Algorithms, Fall 2011

Video thumbnail

P vs. NP - The Biggest Unsolved Problem in Computer Science

Get a free audiobook and a 30-day trial of Audible (and support this channel) at http://www.audible.com/upandatom or text "upandatom" to 500 500 on your phone. Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandat

From playlist Computer Science

Video thumbnail

(8.1) A General Approach to Nonlinear Differential Questions

This video briefly describes the approach to gaining information about the solution to nonlinear differential equations. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

Video thumbnail

The P versus NP problem - Efficient computation and the limits of human knowledge - AVI Wigderson

Speaker : Avi Wigderson ( IAS, Princeton ) Date and Time : 27 Dec 2009, 05:30 PM Venue : J. N. Tata Auditorium, IISc, Bangalore The P vs. NP problem is a central outstanding problem of computer science and mathematics. In this talk I will attempt to describe its technical, scientific and

From playlist Public Lectures

Related pages

Many-one reduction | Oracle machine | If and only if | Function problem | Polynomial hierarchy | Computational complexity theory | Decision problem | NP (complexity) | Quicksort | Complexity class | NP-equivalent