Bibliographic record
Abstract
Nearly thirty years ago, it was shown that \(\Omega (\sqrt {n})\) read/write registers are needed to solve randomized wait-free consensus among n processes. This lower bound was improved to n registers in 2018, which exactly matches known algorithms. The \(\Omega (\sqrt {n})\) space complexity lower bound actually applies to a class of objects called historyless objects, which includes registers, test-and-set objects, and readable swap objects. However, every known n -process obstruction-free consensus algorithm from historyless objects uses Ω ( n ) objects. In this paper, we give the first Ω ( n ) space complexity lower bounds on consensus algorithms for two kinds of historyless objects. First, we show that any obstruction-free consensus algorithm from swap objects uses at least n -1 objects. More generally, we prove that any obstruction-free k -set agreement algorithm from swap objects uses at least \(\lceil \frac{n}{k}\rceil - 1\) objects. The k -set agreement problem is a generalization of consensus in which processes agree on no more than k different output values. This is the first non-constant lower bound on the space complexity of solving k -set agreement with swap objects when k > 1. We also present an obstruction-free k -set agreement algorithm from n-k swap objects, which exactly matches our lower bound when k =1. Second, we show that any obstruction-free binary consensus algorithm from readable swap objects with domain size b uses at least \(\frac{n-2}{3b+1}\) objects. When b is a constant, this asymptotically matches the best known obstruction-free consensus algorithms from readable swap objects with unbounded domains. Since any historyless object can be simulated by a readable swap object with the same domain, our results imply that any obstruction-free consensus algorithm from historyless objects with domain size b uses at least \(\frac{n-2}{3b+1}\) objects. For b = 2, we show a slightly better lower bound of n -2. There is an obstruction-free binary consensus algorithm using 2 n -1 readable swap objects with domain size 2, asymptotically matching our lower bound.
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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 | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".