OpenAI reports a two-fifths-power space simulation for one-tape machines

A fixed deterministic machine with one writable tape can be simulated through a supplied time cap T≥2 in O(T^(2/5) polylog(T+2)) work-space bits while preserving its finite-control and halting outcome.

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Understanding the problem

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A fixed deterministic machine with one writable tape can be simulated through a supplied time cap T≥2 in O(T^(2/5) polylog(T+2)) work-space bits while preserving its finite-control and halting outcome.

Why it matters

If correct, improves the one-tape time-to-space exponent from 1/2 to 2/5.

What counts as progress

Can one-tape time T be simulated in space below the square-root exponent?

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