Many tapes to one

Hopcroft 2e §8.4.2–8.4.3. Extra tapes add no power: a one-tape machine N keeps 2k tracks — each tape’s contents and a marker for where its head is — and simulates one move of M by sweeping right to read under the markers and sweeping left to write and move them. Theorem 8.10 prices it: at most 4n + 2k moves of N per move of M.