Equivalence of two-tape TM and single-tape TM Proof:

Let T =  (Q, Σ, Γ, δ, s) be a 2-tape TM.

We construct a 1-tape TM M=(K, Σ, Γ', δ', s') that

- 

We are required to prove that:

-   if T halts on a with output b, then M halts on a with output b, and if T does not stop on a

• If T loops, then M loops.
• If T hangs in a state p, M hangs anywhere from p to the next state.

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