Turing Machine theory of computation   Design a Turing Machine (M1) that takes any string as input (except the empty string), and shifts each character of the string one place into the right. For instance, if the tape initially contains the following [a|b|a|␣|␣], then it should contain the following after M1 halts [#|a|b|a|␣]. You may assume that M1 always halts and accepts except when the tape does not contain anything. Assume the input alphabet Σ is {a, b} and the tape alphabet Γ is Σ ∪ {#, a, b, ␣}.   a)(30 points) Draw the state diagram for M1.     b)(20 points) Provide the formal definition for M1.

Turing Machine

theory of computation

Design a Turing Machine (M₁) that takes any string as input (except the empty string), and shifts each character of the string one place into the right. For instance, if the tape initially contains the following [a|b|a|␣|␣], then it should contain the following after M₁ halts [#|a|b|a|␣]. You may assume that M₁ always halts and accepts except when the tape does not contain anything.

Assume the input alphabet Σ is {a, b} and the tape alphabet Γ is Σ ∪ {#, a, b, ␣}.

a)(30 points) Draw the state diagram for M₁.

b)(20 points) Provide the formal definition for M₁.

C)(25 points) Describe what M₁ does in numbered stages (as an algorithm).  

d) (25 points) Modify M₁ to make it shift the tape content by two characters instead of one (e.g., the tape content in the previous example should be [#|#|a|b|a|␣]). Redraw the new version of M₁.