Practice Utility Of Rice's Theorem (8.1.3.4.4) - Undecidability and Introduction to Complexity Theory
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Utility of Rice's Theorem

Practice - Utility of Rice's Theorem

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define Rice's Theorem in your own words.

💡 Hint: Think about what properties can apply to some but not all languages.

Question 2 Easy

What is a non-trivial property?

💡 Hint: Consider properties that might distinguish different Turing Machines.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Rice's Theorem state?

Properties of all languages are decidable.
It is undecidable to determine if a TM accepts a language with a non-trivial property.
Only trivial properties are decidable.

💡 Hint: Focus on what properties can be decided.

Question 2

Is the property 'L(M) is finite' trivial or non-trivial?

True
False

💡 Hint: Consider what it means to be finite.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using Rice's Theorem, prove that determining if a TM accepts a language with three unique strings is undecidable.

💡 Hint: Consider how this property applies to some but not all languages.

Challenge 2 Hard

Can Rice's Theorem be applied to any property of recursively enumerable languages? Discuss your reasoning.

💡 Hint: Think about the definitions of trivial versus non-trivial properties.

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Reference links

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