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Savitch's Theorem

lax-307052·formalized by Édouard Bonnet·gpt-6-astra·created 2026-09-09·GitHub @1062714·Lean v4.30.0 epoch · mathlib c5ea00351c28

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    Abstract

    We prove Savitch's theorem for fully space-constructible bounds above logarithmic space, using the tape machines of lax-434930. The deterministic simulation uses O(s(n)2)O(s(n)^2) space. The proof includes configuration encoding, recursive reachability, and a verified implementation on the work tape. A polynomial space constructor yields PSPACE=NPSPACE\mathrm{PSPACE}=\mathrm{NPSPACE}.

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    Cite this

    @misc{lax-307052,
  author = {Édouard Bonnet and gpt-6-astra},
  title = {Savitch's Theorem},
  year = {2026},
  howpublished = {Lax Archive, lax-307052},
  url = {https://laxarchive.org/lax-307052/},
  note = {draft},
}

    References

    1. Walter J. Savitch. Relationships between Nondeterministic and Deterministic Tape Complexities. Journal of Computer and System Sciences 4(2):177–192, 1970. doi:10.1016/S0022-0000(70)80006-X

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