{
  "tag": "WQP1MA",
  "kind": "model",
  "slug": "multitape-turing-machine",
  "name": "Multitape Turing machine",
  "aliases": [
    "k-tape Turing machine"
  ],
  "area": "foundations/models-of-computation",
  "level": "core",
  "summary": "Turing machine with several independent tapes and heads, used to measure running time more naturally.",
  "prereqs": [
    "turing-machine"
  ],
  "sources": [
    {
      "book": "isbn:9781133187790",
      "title": "Michael Sipser, Introduction to the Theory of Computation, third edition",
      "locator": "Section 3.2 (multitape Turing machines) and Section 7.1 (Theorem 7.8, the quadratic simulation)"
    },
    {
      "book": "isbn:9780201530827",
      "title": "Christos H. Papadimitriou, Computational Complexity, Addison-Wesley, 1994",
      "locator": "Section 2.3 (Turing machines with multiple strings) and Section 2.4 (linear speedup)"
    },
    {
      "paper": "doi:10.1090/S0002-9947-1965-0170805-7",
      "title": "Juris Hartmanis and Richard E. Stearns, On the computational complexity of algorithms, Transactions of the American Mathematical Society, volume 117, 1965",
      "locator": "pp. 285 to 306"
    },
    {
      "paper": "doi:10.1145/321356.321362",
      "title": "Frederick C. Hennie and Richard E. Stearns, Two-tape simulation of multitape Turing machines, Journal of the ACM, volume 13, issue 4, 1966",
      "locator": "pp. 533 to 546"
    },
    {
      "paper": "doi:10.1016/S0019-9958(65)90399-2",
      "title": "Frederick C. Hennie, One-tape, off-line Turing machine computations, Information and Control, volume 8, issue 6, 1965",
      "locator": "pp. 553 to 578"
    },
    {
      "paper": "doi:10.1145/322123.322138",
      "title": "Nicholas Pippenger and Michael J. Fischer, Relations among complexity measures, Journal of the ACM, volume 26, issue 2, 1979",
      "locator": "pp. 361 to 381 (the oblivious two-tape simulation and the circuits of size O(t log t))"
    },
    {
      "paper": "doi:10.1145/322003.322015",
      "title": "John Hopcroft, Wolfgang Paul and Leslie Valiant, On time versus space, Journal of the ACM, volume 24, issue 2, 1977",
      "locator": "pp. 332 to 337"
    },
    {
      "paper": "Ryan Williams, Simulating time with square-root space, Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC 2025)",
      "locator": "abstract (the simulation of time t in space O(sqrt(t log t)))"
    },
    {
      "paper": "doi:10.1145/800070.802172",
      "title": "Martin Fürer, The tight deterministic time hierarchy, Proceedings of the 14th Annual ACM Symposium on Theory of Computing (STOC 1982)",
      "locator": "pp. 8 to 16"
    },
    {
      "paper": "doi:10.1109/SFCS.1983.39",
      "title": "Wolfgang J. Paul, Nicholas Pippenger, Endre Szemerédi and William T. Trotter, On determinism versus non-determinism and related problems, 24th Annual Symposium on Foundations of Computer Science (FOCS 1983)",
      "locator": "pp. 429 to 438"
    }
  ],
  "see_also": [
    "multitape-simulation-theorem",
    "linear-speedup-theorem",
    "nondeterministic-turing-machine",
    "random-access-machine",
    "ram-turing-equivalence",
    "palindrome",
    "time-hierarchy-theorem",
    "boolean-circuit"
  ],
  "url": "https://algorithm.tamnd.com/multitape-turing-machine/",
  "path": "nodes/foundations/models-of-computation/multitape-turing-machine",
  "status": {
    "slug": "multitape-turing-machine",
    "h": {
      "level": 0,
      "max": 3,
      "label": "H0",
      "name": "no proof",
      "next": [
        "add a proof in proofs/ (06.5)"
      ]
    },
    "l": {
      "level": 0,
      "max": 4,
      "label": "L0",
      "name": "no Lean part",
      "next": [
        "name a Lean module in the lean field (07)"
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    },
    "i": {},
    "v": {
      "level": 0,
      "max": 3,
      "label": "V0",
      "name": "none",
      "next": [
        "add viz/scene.ts or a figure (10)"
      ]
    },
    "w": {
      "level": 4,
      "max": 5,
      "label": "W4",
      "name": "complete",
      "next": [
        "a review of the text: no review record reviews/WQP1MA/text.yaml"
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  },
  "scene": false
}