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

M = (Q, ∑, I, q0, δ, F) where

- Q - finite, non-empty set of states
- ∑ - finite set of at least 2 symbols: the alphabet. ^ ∈ ∑
- I - non-empty subset of ∑; ^ ∉ I; input alphabet
- q0 - q0 ∈ Q; starting or initial state
- d - δ: (Q\F) x ∑ ⇒Q x ∑ x {-1, 0, 1}, a partial function, the instruction table
- F - F ⊆ Q, the set of final or halting states

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