3 Search Results for "Morris-Wright, Rose"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.14
General Computation Using Slidable Tiles with Deterministic Global Forces

Authors: Alberto Avila-Jimenez, David Barreda, Sarah-Laurie Evans, Austin Luchsinger, Aiden Massie, Robert Schweller, Evan Tomai, and Tim Wylie

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study the computational power of the Full-Tilt model of motion planning, where slidable polyominos are moved maximally around a board by way of a sequence of directional "tilts." We focus on the deterministic scenario in which the tilts constitute a repeated clockwise rotation. We show that general-purpose computation is possible within this framework by providing a direct and efficient simulation of space-bounded Turing machines in which one computational step of the machine is simulated per O(1) rotations. We further show that the initial tape of the machine can be programmed by an initial tilt-sequence preceding the rotations. This result immediately implies new PSPACE-completeness results for the well-studied problems of occupancy (deciding if a given board location can be occupied by a tile), vacancy (deciding if a location can be emptied), relocation (deciding if a tile can be moved from one location to another), and reconfiguration (can a given board configuration be reconfigured into a second given configuration) that hold even for deterministically repeating tilt cycles such as rotations. All of our PSPACE-completeness results hold even when there is only a single domino in the system beyond singleton tiles. Following, we show that these results work in the Single-Step tilt model for larger constant cycles. We then investigate computational efficiency by showing a modification to implement a two-tape Turing machine in the Full-Tilt model and Systolic Arrays in the Single-Step model. Finally, we show a cyclic implementation for tilt-efficient Threshold Circuits.
Cite as

Alberto Avila-Jimenez, David Barreda, Sarah-Laurie Evans, Austin Luchsinger, Aiden Massie, Robert Schweller, Evan Tomai, and Tim Wylie. General Computation Using Slidable Tiles with Deterministic Global Forces. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{avilajimenez_et_al:LIPIcs.ITCS.2026.14,
  author =	{Avila-Jimenez, Alberto and Barreda, David and Evans, Sarah-Laurie and Luchsinger, Austin and Massie, Aiden and Schweller, Robert and Tomai, Evan and Wylie, Tim},
  title =	{{General Computation Using Slidable Tiles with Deterministic Global Forces}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{14:1--14:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.14},
  URN =		{urn:nbn:de:0030-drops-253019},
  doi =		{10.4230/LIPIcs.ITCS.2026.14},
  annote =	{Keywords: motion planning, global control, external forces, deterministic computation, occupancy, vacancy}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.74
Drainability and Fillability of Polyominoes in Diverse Models of Global Control

Authors: Sándor P. Fekete, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Tilt models offer intuitive and clean definitions of complex systems in which particles are influenced by global control commands. Despite a wide range of applications, there has been almost no theoretical investigation into the associated issues of filling and draining geometric environments. This is partly because a globally controlled system (i.e., passive matter) exhibits highly complex behavior that cannot be locally restricted. Thus, there is a strong need for theoretical studies that investigate these models both (1) in terms of relative power to each other, and (2) from a complexity theory perspective. In this work, we provide (1) general tools for comparing and contrasting different models of global control, and (2) both complexity and algorithmic results on filling and draining.
Cite as

Sándor P. Fekete, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer. Drainability and Fillability of Polyominoes in Diverse Models of Global Control. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 74:1-74:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fekete_et_al:LIPIcs.ICALP.2025.74,
  author =	{Fekete, S\'{a}ndor P. and Kramer, Peter and Reinhardt, Jan-Marc and Rieck, Christian and Scheffer, Christian},
  title =	{{Drainability and Fillability of Polyominoes in Diverse Models of Global Control}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{74:1--74:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.74},
  URN =		{urn:nbn:de:0030-drops-234518},
  doi =		{10.4230/LIPIcs.ICALP.2025.74},
  annote =	{Keywords: Global control, full Tilt, single Tilt, Fillability, Drainability, Polyominoes, Complexity}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.16
Tilt: The Video - Designing Worlds to Control Robot Swarms with Only Global Signals

Authors: Aaron T. Becker, Erik D. Demaine, Sándor P. Fekete, Hamed Mohtasham Shad, and Rose Morris-Wright

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract
We present fundamental progress on the computational universality of swarms of micro- or nano-scale robots in complex environments, controlled not by individual navigation, but by a uniform global, external force. More specifically, we consider a 2D grid world, in which all obstacles and robots are unit squares, and for each actuation, robots move maximally until they collide with an obstacle or another robot. The objective is to control robot motion within obstacles, design obstacles in order to achieve desired permutation of robots, and establish controlled interaction that is complex enough to allow arbitrary computations. In this video, we illustrate progress on all these challenges: we demonstrate NP-hardness of parallel navigation, we describe how to construct obstacles that allow arbitrary permutations, and we establish the necessary logic gates for performing arbitrary in-system computations.
Cite as

Aaron T. Becker, Erik D. Demaine, Sándor P. Fekete, Hamed Mohtasham Shad, and Rose Morris-Wright. Tilt: The Video - Designing Worlds to Control Robot Swarms with Only Global Signals. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 16-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{becker_et_al:LIPIcs.SOCG.2015.16,
  author =	{Becker, Aaron T. and Demaine, Erik D. and Fekete, S\'{a}ndor P. and Shad, Hamed Mohtasham and Morris-Wright, Rose},
  title =	{{Tilt: The Video - Designing Worlds to Control Robot Swarms with Only Global Signals}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{16--18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.16},
  URN =		{urn:nbn:de:0030-drops-50870},
  doi =		{10.4230/LIPIcs.SOCG.2015.16},
  annote =	{Keywords: Particle swarms, global control, complexity, geometric computation}
}
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