Practice The Hierarchy Of Languages: Decidable, Recognizable, Undecidable (8.1.4)
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The Hierarchy of Languages: Decidable, Recognizable, Undecidable

Practice - The Hierarchy of Languages: Decidable, Recognizable, Undecidable

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a decidable language.

💡 Hint: Think about how the Turing Machine interacts with inputs.

Question 2 Easy

What is an example of a recognizable language?

💡 Hint: Consider languages that can be accepted by some computational model.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which of the following is true about decidable languages?

They can be accepted by a Turing Machine that loops forever.
They have a Turing Machine that halts on all inputs.
They are a subset of recursively enumerable languages
but may not halt.
There are no known examples.

💡 Hint: Consider the definition of decidability regarding Turing Machines.

Question 2

Is the complement of any recursive language also recursive?

True
False

💡 Hint: Reflect on the relationship between a language and its complement.

3 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Can you construct an example of a Turing Machine that accepts a recognizable language? Describe its components and functionality.

💡 Hint: Think about how the TM processes each character and maintains state.

Challenge 2 Hard

Demonstrate a language that is not recursively enumerable and justify its undecidability.

💡 Hint: Reference the definitions of recursive and recursively enumerable languages to formulate your justification.

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