The Mutual Visibility Problem for Oblivious Robots
Why this work is in the frame
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Bibliographic record
Abstract
Consider a finite set of identical entities, called robots, which can move freely in the Euclidean plane. Let p(t) denote the location of robot p at time t; a robot p can see robot q at time t if at that time no other robot lies in the line segment p(t)q(t). We consider the basic problem called Mutual Visibility: starting from arbitrary distinct locations, within finite time the robots must reach, without collisions, a configuration where they all see each other. This problem must be solved by each entity autonomously executing the same algorithm. We study this problem in the standard model of semi-synchronous oblivious robots. The extensive literature on computability in such a model has never considered this problem because it has always assumed that three collinear robots are mutually visible. In this paper we remove this assumption, and present an algorithm that solves Mutual Visibility. To prove its correctness, we solve a seemingly unrelated problem, Communicating Vessels, which is interesting in its own right. As a byproduct of our solution, we also solve a classical problem for oblivious robots, Near-Gathering, even if one robot is faulty and unable to move.
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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 | 0.006 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.003 |
| Open science | 0.002 | 0.001 |
| 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