10. Computation History Method

TL;DR

The computation history method is used to prove undecidability by showing that certain problems have no solution through mapping reducibilities.

Transcript

[SQUEAKING] [RUSTLING] [CLICKING] MICHAEL SIPSER: Hi, everybody. Can you hear me? Yes. Good. Welcome back to the course. And so we are now at lecture 10, and let's see. What have we been doing? We've been talking about undecidability. So we introduced, last time, reducibilities and mapping reducibilities for proving various problems are undecidable... Read More

Key Insights

• 👍 The computation history method is a widely used approach for proving undecidability.

Questions & Answers

Q: How do you prove that a language is undecidable?

To prove that a language is undecidable, you need to reduce a known undecidable problem to the problem you're trying to prove undecidable.

Q: What is the computation history method?

The computation history method involves creating a sequence of configurations in a computation to prove a problem's undecidability.

Q: How do you use the computation history method to prove undecidability?

The computation history method involves showing that a known undecidable problem is reducible to the problem you're trying to prove undecidable, typically by constructing a matching problem.

Q: Why do we need to use the computation history method for undecidability proofs?

The computation history method is used in undecidability proofs to show that a language is undecidable by demonstrating that no algorithm can solve the problem. It provides a formal and rigorous approach to proving undecidability.

Summary & Key Takeaways

• The undecidability of a problem is proven by showing that a known undecidable problem is reducible to the problem in question.

• The computation history method is a widely used approach for proving undecidability, particularly in more complex cases.

• The post correspondence problem (PCP), which involves finding a match among pairs of strings, is used to illustrate the computation history method.