Step-optimal implementations of large single-writer registers
Bibliographic record
Abstract
We present two wait-free algorithms for simulating an ℓ-bit single-writer register from k-bit single-writer registers, for any k≥1. Our first algorithm has Θ(ℓ/k) step complexity for both and and uses Θ(4ℓ−k) registers. Our second algorithm has Θ(ℓ/k+(logn)/k) step complexity for both and , where n is the number of readers, but uses only Θ(nℓ/k) registers. By using the first algorithm when ℓ≤(logn)/2 and the second algorithm when ℓ>(logn)/2, we get a combined implementation with Θ(ℓ/k) step complexity using Θ(nℓ/k) registers which works for any 1≤k<ℓ. We also prove that any implementation with O(ℓ/k) step complexity for requires Ω(ℓ/k) step complexity for . Reading ℓ bits requires at least ⌈ℓ/k⌉ reads of k-bit registers, so our lower bound shows that our combined implementation is step-optimal.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".