Lower bounds for adaptive collect and related objects
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Bibliographic record
Abstract
An adaptive algorithm, whose step complexity adjusts to the number of active processes, is attractive for situations in which the number of participating processes is highly variable. This paper studies the number and type of multi-writer registers that are needed for adaptive algorithms. We prove that if a collect algorithm is f -adaptive to total contention, namely, its step complexity is f(k), where k is the number of processes that ever took a step, then it uses Ω(f-1(n) multi-writer registers, where n is the total number of processes in the system.Furthermore, we show that competition for the underlying registers is inherent for adaptive collect algorithms. We consider c-write registers, to which at most c processes can be concurrently about to write. Special attention is given to exclusive-write registers, the case c=1 where no competition is allowed, and concurrent-write registers, the case c=n where any amount of competition is allowed. A collect algorithm is f-adaptive to point contention, if its step complexity is f(k), where k is the maximum number of simultaneously active processes. Such an algorithm is shown to require Ω(f-1 (n<over>c)) concurrent-write registers, even if an unlimited number of c-write registers are available. A smaller lower bound is also obtained in this situation for collect algorithms that are f-adaptive to total contention.The lower bounds also hold for nondeterministic implementations of sensitive objects from historyless objects.Finally, we present lower bounds on the step complexity in solo executions (i.e., without any contention), when only c-write registers are used: For weak test&set objects, we present an Ω(log n<over>log c +log log n) lower bound. Our lower bound for collect and sensitive objects is Ω(n-1<over>c).
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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 | 0.000 |
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 it