The Space Complexity of Long-Lived and One-Shot Timestamp Implementations
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Bibliographic record
Abstract
This article is concerned with the problem of implementing an unbounded timestamp object from multiwriter atomic registers, in an asynchronous distributed system of n processes with distinct identifiers where timestamps are taken from an arbitrary universe. Ellen et al. [2008] showed that √ n /2 − O (1) registers are required for any obstruction-free implementation of long-lived timestamp systems from atomic registers (meaning processes can repeatedly get timestamps). We improve this existing lower bound in two ways. First we establish a lower bound of n /6 − 1 registers for the obstruction-free long-lived timestamp problem. Previous such linear lower bounds were only known for constrained versions of the timestamp problem. This bound is asymptotically tight; Ellen et al. [2008] constructed a wait-free algorithm that uses n − 1 registers. Second we show that √2 n − log n − O (1) registers are required for any obstruction-free implementation of one-shot timestamp systems (meaning each process can get a timestamp at most once). We show that this bound is also asymptotically tight by providing a wait-free one-shot timestamp system that uses at most ⌈2√ n ⌉ registers, thus establishing a space complexity gap between one-shot and long-lived timestamp systems.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it