The Deepest Unanswered Question in Computer Science: P vs. NP

💡The P vs. NP problem is the most recently conceived and easiest-to-understand question among the Millennium Prize problems.

🧩Sudoku and protein folding are examples of NP-complete problems, which are among the most challenging computational tasks.

🚀Finding a solution to the P vs. NP problem could lead to major advancements in various fields, including cancer research and encryption.

🔍P vs. NP explores the relationship between problems solvable by fast programs (P) and problems that can be efficiently checked (NP).

🔐The difficulty of proving P vs. NP stems from the complexity of the problem itself, as proving things is also an NP problem.

What is the P vs. NP problem?

—The P vs. NP problem explores whether problems with quick solutions (P) also have quick methods to find those solutions (NP). It aims to determine if all problems that are efficiently verifiable are also efficiently solvable.

Why is P vs. NP important?

—Solving P vs. NP could have far-reaching implications. If P = NP, it means fast solutions exist for all challenging problems, which would revolutionize fields like biology, economics, and cryptography. If P ≠ NP, it implies fundamental differences between verification and solution finding.

Are all NP problems also in P?

—It is unknown whether all NP problems are in P. If they are, it means fast solutions exist for all problems that can be efficiently verified. However, if some NP problems are harder than those in P, it implies the existence of unsolvable problems.

What are NP-complete problems?

—NP-complete problems are a subset of NP problems that are at least as hard as the hardest problems in NP. Solving one NP-complete problem would enable solving all NP problems efficiently. Sudoku and protein folding are examples of NP-complete problems.

How does P vs. NP relate to everyday life?

—The P vs. NP problem impacts everyday life by challenging the limits of computation. Solving it would lead to advancements in solving puzzles, improving medical research, enhancing economic models, and ensuring secure encryption algorithms.

00:01The P vs. NP problem is considered the deepest unanswered question in computer science and math.

00:09The Clay Institute offered a prize for solving the seven Millenium Prize problems, including P vs. NP.

00:41P vs. NP asks whether problems that are efficiently verifiable can also be efficiently solvable.

02:14NP problems have polynomial time checking, while P problems have polynomial time solutions.

03:58Solving P vs. NP could have significant implications for biology, economics, and encryption.

05:51Sudoku and protein folding are examples of NP-complete problems.

09:59The P vs. NP problem has connections to the nature of computation, space, and time.

09:46Solving P vs. NP may revolutionize our understanding of the world and impact various fields.