# 14. P and NP, SAT, Poly-Time Reducibility | Summary and Q&A

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October 6, 2021
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14. P and NP, SAT, Poly-Time Reducibility

## TL;DR

The lecture discusses the P vs NP problem and introduces the concept of dynamic programming.

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### Q: What is the relationship between deterministic and non-deterministic models in complexity theory?

Deterministic and non-deterministic models are different ways of measuring complexity, but they can both be used to solve the same types of problems. Non-deterministic models allow for parallel computation, while deterministic models operate sequentially.

### Q: What is the significance of the P vs NP problem?

The P vs NP problem is one of the most famous unsolved problems in computer science. It asks whether every problem that can be verified in polynomial time can also be solved in polynomial time. If P equals NP, it would have profound implications for the efficiency of algorithms and the security of cryptographic systems.

### Q: What is dynamic programming and how is it useful?

Dynamic programming is an algorithmic technique that solves complex problems by breaking them down into smaller overlapping subproblems. It is useful for solving optimization problems and can often lead to more efficient algorithms.

### Q: How is satisfiability (SAT) related to the P vs NP problem?

The SAT problem is a fundamental problem in computer science that asks whether a given Boolean formula can be satisfied. It is known to be in NP, and if it can be solved in polynomial time, it would imply that all problems in NP can also be solved in polynomial time.

## Summary & Key Takeaways

• The lecture starts with a review of complexity theory and the relationship between deterministic and non-deterministic models.

• The concept of time complexity classes, specifically P and NP, is introduced and explained.

• The lecture then focuses on dynamic programming, a fundamental algorithmic technique, and its application to the A CFG problem.

• The concept of satisfiability (SAT) is introduced as a way to determine if a Boolean formula is true or false, and its connection to the P vs NP problem is discussed.