Describe the functionality of tm2 in natural language

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Reference no: EM133254205

Exercise 1 (Theory & Proofs)

Answer the following.
Question 1. Consider a language L₀ that is enumerated by a Turing Machine TM₀. Is it possible to create a Turing Machine TM6 that only accepts strings in L₀, instead?
Question 2. Consider a Turing Machine TM_s, which simulates a k-tape Turing Machine TM_k. Show that if nth has polynomial time complexity, so does its simulation.

Exercise 2 (Turing Machine Variations)
Consider the language L₁ = {a*aⁱb*bⁱ i N}. Construct a 2-tape Turing Machine TM1 that accepts L₁.
Question 1. Provide three examples of 1 ∈ L₁.
Question 2. Describe the functionality of TM₁in natural language.
Question 3. Provide a state diagram for TM₁.
Question 4. State and justify the complexity of TM₁.

Exercise 3 (Language Enumerating Turing Machines)
Consider a language L₂ = {a^2k | k ∈ N}. Construct a language-enumerating k - tape Turing Machine that enumerates L₂.
Question 1. Provide three examples of 1 ∈ L₂.
Question 2. Choose a value for k and justify it.
Question 3. Describe the functionality of TM₂ in natural language.
Question 4. Provide a state diagram for TM₂.
Question 5. State and justify the complexity of TM₂.

Exercise 4 (Non-deterministic Turing Machine) We call a number x composite if it is not prime. That is, x is composite if it can be represented as a product of natural numbers n, m E N and n, m > 1. Construct a non-deterministic Turing Machine that accepts strictly the language composed of the unary representation of composite numbers. Recall the unary representation of natural numbers, i.e., 5 → 111111.
1. Describe the Turing Machine in natural language.
2. Draw a state diagram for M_L,3.

Attachment:- Turing Machine Variations.rar

Reference no: EM133254205

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