On the power of bounded asynchrony: convergence by autonomous robots with limited visibility
Bibliographic record
Abstract
Abstract A distributed algorithm $${\mathcal {A}}$$ A solves the Point Convergence task if an arbitrarily large collection of entities, starting in an arbitrary configuration, move under the control of $${\mathcal {A}}$$ A to eventually form and thereafter maintain configurations in which the separation between all entities is arbitrarily small. This fundamental task in the standard $$\mathcal {OBLOT}$$ OBLOT model of autonomous mobile entities has been previously studied in a variety of settings, including full visibility, exact measurements (including distances and angles), and synchronous activation of entities. Our study concerns the minimal assumptions under which entities, moving asynchronously with limited and unknown visibility range and subject to limited imprecision in measurements, can be guaranteed to converge in this way. We present an algorithm operating under these constraints that solves Point Convergence, for entities moving in two or three dimensional space, with any bounded degree of asynchrony. We also prove that under similar realistic constraints, but unbounded asynchrony, Point Convergence in the plane is not possible in general, contingent on the natural assumption that algorithms maintain the (visible) connectivity among entities present in the initial configuration. This variant, that we call Cohesive Convergence, serves to distinguish the power of bounded and unbounded asynchrony in the control of autonomous mobile entities, settling a long-standing question whether in the Euclidean plane synchronously scheduled entities are more powerful than asynchronously scheduled entities.
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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 | 0.005 | 0.037 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".