Practice Turing Machines with Semi-Infinite Tape - 4.5 | Module 7: Turing Machines and Computability | Theory of Computation
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4.5 - Turing Machines with Semi-Infinite Tape

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is a semi-infinite tape Turing Machine?

πŸ’‘ Hint: Consider how its tape differs from a traditional Turing Machine's tape.

Question 2

Easy

Explain the term 'equivalence' in the context of Turing Machines.

πŸ’‘ Hint: Think about how varying structures still achieve the same computations.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What defines a semi-infinite tape Turing Machine?

  • It has a fixed leftmost cell and extends rightward indefinitely.
  • It has a fixed rightmost cell and extends leftward indefinitely.
  • It has two read/write heads.

πŸ’‘ Hint: Focus on the fixed point and the direction of extension.

Question 2

True or False: A semi-infinite tape Turing Machine can be represented as equivalent to a two-way infinite tape Turing Machine.

  • True
  • False

πŸ’‘ Hint: Think about how computational capabilities are maintained despite structural differences.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Construct a Turing Machine with a semi-infinite tape and describe how it would process an input string that requires checking patterns in both left and right halves of a two-way infinite TM.

πŸ’‘ Hint: Visualize both tracks and how movements simulate two-way functionalities.

Question 2

Explain how the structure of a semi-infinite tape Turing Machine could affect the type of problems it can compute compared to a standard Turing Machine.

πŸ’‘ Hint: Think about how the fixed leftmost cell could impede certain problem approaches.

Challenge and get performance evaluation