Bibliographic record
Abstract
Herlihy's wait-free consensus hierarchy classifies the power of object types in asynchronous shared memory systems where processes can permanently crash (i.e. stop taking steps). In this hierarchy a type has consensus number n if objects of that type can be used along with (read/write) registers to solve consensus among n processes that can permanently crash, but not among n + 1 or more processes. In systems where processes can recover after crashing, the power of an object type to solve consensus may be different. Golab's recoverable consensus hierarchy classifies the power of object types in such a system. In the recoverable consensus hierarchy, a type has recoverable consensus number n if objects of that type can be used along with registers to solve consensus among n processes that can recover after crashing, but not among n + 1 or more processes. In this paper, we prove that the recoverable consensus hierarchy of deterministic, readable types is robust, i.e., if consensus can be solved among n processes that can recover after crashing using a collection of objects of deterministic, readable types, then one of these types has recoverable consensus number at least n. This is important for comparing the relative computational power of different deterministic, readable types, because it implies that one cannot combine various objects to obtain an algorithm that is better at solving recoverable consensus than any of the individual object types. Our result can be used to show that, for all n ≥ 4, there exists a readable type with consensus number n and recoverable consensus number n − 2. We also show that, for all n > n′ ≥ 1, there exists a non-readable type that has consensus number n and recoverable consensus number n′.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".