A separation of (n -1)-consensus and n-consensus in read-write shared-memory systems
Bibliographic record
Abstract
A fundamental research theme in distributed computing is the comparison of systems in terms of their ability to solve basic problems such as consensus that cannot be solved in completely asynchronous systems. In particular, in a seminal work [14], Herlihy compares shared-memory systems in terms of the shared objects that they have: he proved that there are shared objects that are powerful enough to solve consensus among n processes, but are too weak to solve consensus among n + 1 processes; such objects are placed at level n of a wait-free hierarchy. The importance of this hierarchy comes from Herlihy's universality result: intuitively, every object at level n of this hierarchy can be used to implement any object shared by n processes in a wait-free manner. As in [14], we compare shared-memory systems with respect to their ability to solve consensus among n processes. But instead of comparing systems defined by the shared objects that they have, we compare readwrite systems defined by the process schedules that they allow. These systems capture a large set of systems, e.g., systems whose synchrony ranges from fully synchronous to completely asynchronous, several systems with failure detectors, and "obstruction-free" systems. In this paper, we consider read-write systems defined in terms of process schedules, and investigate the following natural question: For every n, is there a system of n processes that is strong enough to solve consensus among every subset of n -1 processes in the system, but not enough to solve consensus among all the n processes of the system? We show that the answer to the above question is "yes", and so these systems can be classified into hierarchy akin to Herlihy's hierarchy.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".