Does P=NP? | Richard Karp and Lex Fridman | Summary and Q&A

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July 29, 2020
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Does P=NP? | Richard Karp and Lex Fridman

TL;DR

The central problem in computer science is the question of whether P is equal to NP, which has significant implications for solving complex problems efficiently.

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Questions & Answers

Q: What is the P vs NP problem and why is it considered the central problem in computer science?

The P vs NP problem asks whether problems that can be verified in polynomial time can also be solved in polynomial time. It is the central problem in computer science because it has major implications for efficiency in solving complex problems.

Q: Why do many researchers believe that P is not equal to NP?

There is a belief that P is not equal to NP because many well-studied problems, such as factoring large numbers, do not have efficient solutions. Despite intense research, no polynomial time algorithms have been found for these problems.

Q: What are the implications if P is equal to NP?

If P is equal to NP, it would mean that every problem with a quick verification process can be solved efficiently. This would have significant implications for fields like scheduling, cryptography, and optimization.

Q: Are there any results or evidence regarding the P vs NP problem?

Some results suggest that if P is not equal to NP, then many well-known combinatorial problems cannot be solved in polynomial time. These results build upon earlier work by mathematician Stephen Cook and provide insights into the relationship between P and NP.

Summary & Key Takeaways

  • The P vs NP problem is about determining whether problems that can be quickly verified also have efficient solutions.

  • There is a strong belief that P is not equal to NP due to the lack of efficient algorithms for well-studied problems like factoring large numbers.

  • Finding an efficient algorithm for these problems would have significant implications in various fields.

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