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Exact logarithmic-space derandomization

Restricted randomized log-space models and simulations using more than logarithmic space do not establish exact log-space derandomization.

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Understanding the problem

Read the background

Restricted randomized log-space models and simulations using more than logarithmic space do not establish exact log-space derandomization. The target is equality of these decision classes.

The theorem concerns polynomial-time log-space machines in the stated model. It does not establish P=BPP or eliminate randomness from every polynomial-time algorithm.

Why it matters

If correct, closes the stated deterministic-versus-randomized logarithmic-space gap.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The theorem concerns polynomial-time log-space machines in the stated model. It does not establish P=BPP or eliminate randomness from every polynomial-time algorithm.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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