# The status of the P versus NP problem

@article{Fortnow2009TheSO, title={The status of the P versus NP problem}, author={Lance Fortnow}, journal={Commun. ACM}, year={2009}, volume={52}, pages={78-86} }

It's one of the fundamental mathematical problems of our time, and its importance grows with the rise of powerful computers.

## 278 Citations

Mathematics in the age of the Turing machine

- Computer ScienceTuring's Legacy
- 2014

The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs, as well as some examples from the literature.

Inductive Complexity of P versus NP Problem - Extended Abstract

- MathematicsUCNC
- 2012

An upper bound on the inductive complexity of second order of the P versus NP problem is determined using the complexity measure developed in [7,3,4] and the extensions obtained by using inductive register machines of various orders in [1,2].

A Simple Proof of P versus NP

- Mathematics
- 2018

P versus NP is one of the most important and unsolved problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? Another major complexity class is…

QP versus NP

- Computer Science
- 2018

It is proved that maximum exclusive-or 2-satisﬁability is in QP, and it is demonstrated this problem is NP-complete.

An Interesting Perspective to the P versus NP Problem

- Mathematics
- 2015

We discuss the P versus NP problem from the perspective of addition operation about polynomial functions. Two contradictory propositions for the addition operation are presented. With the proposition…

On the P VS NP Question: A New Proof of Inequality

- Computer Science, Mathematics
- 2021

It is proved that the cost of the minimal implementation of core function increases with n exponentially, which is equivalent to proving that P and NP do not coincide.

The complexity of class polyL

- Computer Science
- 2018

Since every language in polyL is in QP, then every problem in NP can be decided in a quasi-polynomial time.

The P = Sharp-P Consequence

- Computer Science
- 2018

It is proved if Sharp-P = P, then it can be determined in polynomial time which subsets could be solved in a feasible polynometric time from every EXP language.

Quadratic Congruences on Average Case

- Computer Science
- 2018

The Quadratic Congruences is a known NP-complete problem and it is shown this problem can be solved in polynomial time for the average case.

On Average Case

- Computer Science
- 2017

There is an NP-complete problem that can be solved in polynomial time for the average case and the concept of NP-completeness has been very useful.

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The paper attempts to summarize the state of knowledge in this area, including some "folklore" results that have not explicitly appeared in print, and tries to standardize and unify definitions.

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