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Computational Power of Opaque Robots

Caterina Feletti, Lucia Mambretti, Carlo Mereghetti, Beatrice Palano

TL;DR

The paper advances the taxonomy of distributed computation by opaque, collision-intolerant mobile robots in the look–compute–move model, extending prior transparent analyses to obstructed visibility. It formalizes 12 opaque models across three synchronization modes and introduces six witness problems to map dominance, equivalence, and orthogonality relations, revealing how obstruction interacts with memory and communication. The results show that transparency strictly enhances computational power and that constant-size lights cannot always overcome visibility limitations, with notable phenomena such as false elections under asynchrony. The relation map and open questions, including LUMI^S versus LUMI^A equivalence, provide a foundation for future work on the full hierarchy and the impact of obstructed visibility on distributed robotics.

Abstract

In the field of distributed computing by robot swarms, the research comprehends manifold models where robots operate in the Euclidean plane through a sequence of look-compute-move cycles. Models under study differ for (i) the possibility of storing constant-size information, (ii) the possibility of communicating constant-size information, and (iii) the synchronization mode. By varying features (i,ii), we obtain the noted four base models: OBLOT (silent and oblivious robots), FSTA (silent and finite-state robots), FCOM (oblivious and finite-communication robots), and LUMI (finite-state and finite-communication robots). Combining each base model with the three main synchronization modes (fully synchronous, semi-synchronous, and asynchronous), we obtain the well-known 12 models. Extensive research has studied their computational power, proving the hierarchical relations between different models. However, only transparent robots have been considered. In this work, we study the taxonomy of the 12 models considering collision-intolerant opaque robots. We present six witness problems that prove the majority of the computational relations between the 12 models. In particular, the last witness problem depicts a peculiar issue occurring in the case of obstructed visibility and asynchrony.

Computational Power of Opaque Robots

TL;DR

The paper advances the taxonomy of distributed computation by opaque, collision-intolerant mobile robots in the look–compute–move model, extending prior transparent analyses to obstructed visibility. It formalizes 12 opaque models across three synchronization modes and introduces six witness problems to map dominance, equivalence, and orthogonality relations, revealing how obstruction interacts with memory and communication. The results show that transparency strictly enhances computational power and that constant-size lights cannot always overcome visibility limitations, with notable phenomena such as false elections under asynchrony. The relation map and open questions, including LUMI^S versus LUMI^A equivalence, provide a foundation for future work on the full hierarchy and the impact of obstructed visibility on distributed robotics.

Abstract

In the field of distributed computing by robot swarms, the research comprehends manifold models where robots operate in the Euclidean plane through a sequence of look-compute-move cycles. Models under study differ for (i) the possibility of storing constant-size information, (ii) the possibility of communicating constant-size information, and (iii) the synchronization mode. By varying features (i,ii), we obtain the noted four base models: OBLOT (silent and oblivious robots), FSTA (silent and finite-state robots), FCOM (oblivious and finite-communication robots), and LUMI (finite-state and finite-communication robots). Combining each base model with the three main synchronization modes (fully synchronous, semi-synchronous, and asynchronous), we obtain the well-known 12 models. Extensive research has studied their computational power, proving the hierarchical relations between different models. However, only transparent robots have been considered. In this work, we study the taxonomy of the 12 models considering collision-intolerant opaque robots. We present six witness problems that prove the majority of the computational relations between the 12 models. In particular, the last witness problem depicts a peculiar issue occurring in the case of obstructed visibility and asynchrony.
Paper Structure (12 sections, 24 theorems, 25 equations, 3 figures, 6 tables)

This paper contains 12 sections, 24 theorems, 25 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Models
  4. Problems
  5. Computational Relations
  6. Transparent vs opaque robots
  7. Taxonomy of opaque models
  8. Weakness of $\overline{\mathcal{OBLOT}}^{\mathtt{}}$
  9. Orthogonality between $\overline{\mathcal{FSTA}}^\mathtt{}$ and $\overline{\mathcal{FCOM}}^\mathtt{}$
  10. Power of FULLY
  11. Opaqueness and asynchrony
  12. Relation map

Key Result

Theorem 1

Let $P$ be a problem solved in $\overline{X}^Y$. Then $P$ is solved under ${X}^Y$.

Figures (3)

  • Figure 1: Line-Stretch.
  • Figure 2: The safe zone of the square comprehends all the points not belonging to the blue-colored (infinite) lines and zones.
  • Figure 3: The Pseudo-Polygon problem associated with an octagon.

Theorems & Definitions (42)

  • Theorem 1
  • proof
  • Corollary 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • ...and 32 more