The transition function δ in a multi-tape Turing machine (k tapes) is defined as:

1. Aδ : 2^Q × Γ^k → 2^Q × Γ^k × {L, R, S}^k
2. Bδ : Q × Q × Γ^k → Q × Q × Γ^k × {L, R, S}^k
3. Cδ : Q × Γ^k → Q × Γ^k × {L, R, S}^k
4. Dδ : Q × Γ^k × 2^Q → Q × Γ^k × 2^Q × {L, R, S}^k

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