Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 137-01. Simulating One-Tape Time in Two-Fifths-Power Space
Manuscript map · lines 5055–5064
OpenAI@2026-10-07#rem:oai-p-137-01
Authors: OpenAI. Family 137.
Title: Simulating One-Tape Time in Two-Fifths-Power Space.
Abstract: We show that a fixed deterministic Turing machine with one writable tape and head can be simulated in $O(T{}{2/5}{}mathop{{}mathrm{polylog}}{}nolimits (T+2))$ work-space bits when a binary time cap T ≥ 2 is supplied. The simulator computes the finite-control and halting outcome by time T; its running time is unrestricted. The result allows a fixed number of read-only input heads and requires a fixed accessor that supplies every initial writable and read-only symbol within distance T of the relevant head origin in polylogarithmic space. This improves the square-root space exponent for one-tape machines, answering Williams's question for this model.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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