The Space Complexity of Asynchronous Algorithms from Bounded Size Base Objects
Bibliographic record
Abstract
In this thesis, we consider distributed algorithms that use base objects with bounded domain sizes. Since real distributed systems have base objects with bounded domain sizes, such algorithms are more practical. Considering systems with bounded size base objects also gives us more power to prove new space complexity lower bounds. We devise a new technique for obtaining space complexity lower bounds for obstruction-free algorithms that use bounded size base objects. First, we consider obstruction-free implementations of scannable objects, which consist of a sequence of components that can be read simultaneously. More specifically, we consider scannable objects whose components are fully reusable, which means that, for every pair of values v, v' of a component, there is a sequence of operations which changes the value of that component from v to v'. When k >= 1 and 2^k - 2^(k-r) <= n-1 < 2^k - 2^(k-r-1), we show that any obstruction-free, n-process implementation of a scannable object with k fully reusable components that have domain {0, 1} requires at least n+k-r-2 base objects with domain {0, 1}. We also generalize our technique to obtain new space complexity lower bounds for scannable objects that have fully reusable components with possibly different bounded domain sizes. Next, we obtain new lower bounds for obstruction-free consensus algorithms from readable swap objects with bounded domain sizes. We show that at least n-2 readable swap objects with domain {0, 1} are needed to solve obstruction-free consensus among n processes, asymptotically matching the best known upper bounds. When using readable swap objects with domain size b, we show that at least (n-2)/(3b+1) objects are needed. Finally, we investigate the space complexity of solving obstruction-free k-set agreement from swap objects. For all n > k >= 1, we show that ceil(n/k) - 1 swap objects are needed to solve obstruction-free k-set agreement among n processes. We also give an obstruction-free k-set agreement algorithm that uses n-k swap objects, which exactly matches our lower bound for k = 1.
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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 | 0.004 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.012 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 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".