Bibliographic record
Abstract
Since the early days of the shared memory model for distributed computing, researchers have sought a simple and precise characterization of an object’s ability to implement other objects in a wait-free manner. The first candidate for such a characterization was the consensus number of an object [24]. But a characterization based on consensus numbers is not precise: there are pairs of objects with the same consensus number that are not equivalent (i.e., one object cannot be wait-free implemented by instances of the other and registers) [2, 42]. A more recent candidate for such a characterization is the set agreement power of an object [15]. In this thesis, we show that this characterization is not precise even for the case of deterministic objects: there are pairs of deterministic objects with the same set agreement power that are not equivalent. Next, we show that there are uncountably many objects with distinct set agreement power. Consequently, a precise characterization of an object’s ability to implement other objects in a wait-free manner must classify objects into uncountably many cells. This suggests that there is no simple and precise characterization of objects, since the cells of an uncountable classification cannot be labeled using simple integers (as in Herlihy’s hierarchy) or even finite sequences of integers. Finally, we introduce a generalization of consensus called bounded disagreement, which differs from set agreement in that it restricts the number of disagreeing processes rather than the number of disagreeing values. More precisely, the l-bounded disagreement task for n processes has the following requirement: there is a value v such that at most l processes (the disagreers) decide values that are not v. We then show that for every integer n ≥ 2, there is a bounded disagreement object that has consensus number n, but is not equivalent to the n-consensus object. Prior to this work, the only objects known to have this unusual characteristic for n ≥ 2 (which shows that the characterization of objects via consensus numbers is not precise) were artificial objects crafted solely for the purpose of exhibiting this behaviour [2, 42].
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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 | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".