Solution

The correct answer is δ : Q × Γk → Q × Γk × {L, R, S}k

Key Points

• The transition function for a multi-tape Turing machine should define the result of being in a certain state and reading a certain symbol or symbols from the tapes.The correct definition should be
• δ : Q × Γ^k → Q × Γ^k × {L, R, S}^k
• Here is what each part of the transition function means:
  • Q × Γk : The Turing machine is in a certain state from its set of states Q and reads from its k tapes symbols from the tape alphabet Γ.
  • → : This is the function mapping that describes that the left-hand side leads to the right-hand side.
  • Q × Γk × {L, R, S}k : The Turing machine moves into a new state from its set of states Q, writes symbols onto its k tapes from the tape alphabet Γ, and moves its k tape heads either one cell to the left (L), one cell to the right (R), or stays stationary (S).