A Turing Machine has a 6-tuple representation as given below

M = (Q, ∑, I, q0, δ, F) where

1. Q - finite, non-empty set of states

2. ∑ - finite set of at least 2 symbols: the alphabet. ^ ∈ ∑

3. I - non-empty subset of ∑; ^ ∉ I; input alphabet

4. q0 - q0 ∈ Q; starting or initial state

5. d - δ: (Q\F) x ∑ ⇒Q x ∑ x {-1, 0, 1}, a partial function, the instruction table

6. F - F ⊆ Q, the set of final or halting states