12. Time Complexity

TL;DR

The class P is a collection of languages that can be decided in polynomial time on a one tape Turing machine.

Transcript

[SQUEAKING] [RUSTLING] [CLICKING] MICHAEL SIPSER: So welcome, everybody. Welcome back. Let's get started with today's lecture. Where were we? On Tuesday, we covered, the main topic was the recursion theorem, which allows programs to self-reference. And we saw some applications of that, too. So we gave a new proof that ATM is undecidable. We looked ... Read More

Key Insights

• 🛫 The class P is a collection of languages that can be decided in polynomial time on a one tape Turing machine.
• 🎩 The class P is invariant for all reasonable deterministic models.
• 🎩 The class P is important because it captures problems that can be solved in a reasonable practical sense.

Questions & Answers

Q: What is the class P?

The class P is a collection of languages that can be decided in polynomial time on a one tape Turing machine.

Q: Are all reasonable deterministic models polynomially related?

Yes, all reasonable deterministic models are polynomially related, meaning they can simulate each other with, at most, a polynomial overhead.

Summary & Key Takeaways

• The lecture introduces complexity theory and computational complexity.

• It explains the difference between the models used in computability theory and complexity theory.

• The class P is introduced as the collection of languages that can be decided in polynomial time on a one tape Turing machine.