The Space Complexity of Long-Lived and One-Shot Timestamp Implementations
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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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 | 0.004 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.005 | 0.015 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".