The transition function 'δ' in multi-tape Turing machine is defined as: 

1
δ : 2Q × Γk → 2Q × Γk × {L, R, S}k
2
δ : Q × Q × Γk → Q × Q × Γk × {L, R, S}k
3
δ : Q × Γk → Q × Γk × {L, R, S}k
4
δ : Q × Γk × 2Q → Q × Γk × 2Q × {L, R, S}k

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