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Documents authored by Diomidov, Yevhenii

Document
DOI: 10.4230/LIPIcs.SAND.2023.5
Complexity of Motion Planning of Arbitrarily Many Robots: Gadgets, Petri Nets, and Counter Machines

Authors: Joshua Ani, Michael Coulombe, Erik D. Demaine, Yevhenii Diomidov, Timothy Gomez, Dylan Hendrickson, and Jayson Lynch

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
We extend the motion-planning-through-gadgets framework to several new scenarios involving various numbers of robots/agents, and analyze the complexity of the resulting motion-planning problems. While past work considers just one robot or one robot per player, most of our models allow for one or more locations to spawn new robots in each time step, leading to arbitrarily many robots. In the 0-player context, where all motion is deterministically forced, we prove that deciding whether any robot ever reaches a specified location is undecidable, by representing a counter machine. In the 1-player context, where the player can choose how to move the robots, we prove equivalence to Petri nets, EXPSPACE-completeness for reaching a specified location, PSPACE-completeness for reconfiguration, and ACKERMANN-completeness for reconfiguration when robots can be destroyed in addition to spawned. Finally, we consider a variation on the standard 2-player context where, instead of one robot per player, we have one robot shared by the players, along with a ko rule to prevent immediately undoing the previous move. We prove this impartial 2-player game EXPTIME-complete.
Cite as

Joshua Ani, Michael Coulombe, Erik D. Demaine, Yevhenii Diomidov, Timothy Gomez, Dylan Hendrickson, and Jayson Lynch. Complexity of Motion Planning of Arbitrarily Many Robots: Gadgets, Petri Nets, and Counter Machines. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ani_et_al:LIPIcs.SAND.2023.5,
  author =	{Ani, Joshua and Coulombe, Michael and Demaine, Erik D. and Diomidov, Yevhenii and Gomez, Timothy and Hendrickson, Dylan and Lynch, Jayson},
  title =	{{Complexity of Motion Planning of Arbitrarily Many Robots: Gadgets, Petri Nets, and Counter Machines}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.5},
  URN =		{urn:nbn:de:0030-drops-179414},
  doi =		{10.4230/LIPIcs.SAND.2023.5},
  annote =	{Keywords: Gadgets, robots, undecidability, Petri nets}
}
Document
DOI: 10.4230/LIPIcs.FUN.2022.3
Pushing Blocks via Checkable Gadgets: PSPACE-Completeness of Push-1F and Block/Box Dude

Authors: Joshua Ani, Lily Chung, Erik D. Demaine, Yevhenii Diomidov, Dylan Hendrickson, and Jayson Lynch

Published in: LIPIcs, Volume 226, 11th International Conference on Fun with Algorithms (FUN 2022)

Abstract
We prove PSPACE-completeness of the well-studied pushing-block puzzle Push-1F, a theoretical abstraction of many video games (first posed in 1999). We also prove PSPACE-completeness of two versions of the recently studied block-moving puzzle game with gravity, Block Dude - a video game dating back to 1994 - featuring either liftable blocks or pushable blocks. Two of our reductions are built on a new framework for "checkable" gadgets, extending the motion-planning-through-gadgets framework to support gadgets that can be misused, provided those misuses can be detected later.
Cite as

Joshua Ani, Lily Chung, Erik D. Demaine, Yevhenii Diomidov, Dylan Hendrickson, and Jayson Lynch. Pushing Blocks via Checkable Gadgets: PSPACE-Completeness of Push-1F and Block/Box Dude. In 11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 3:1-3:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ani_et_al:LIPIcs.FUN.2022.3,
  author =	{Ani, Joshua and Chung, Lily and Demaine, Erik D. and Diomidov, Yevhenii and Hendrickson, Dylan and Lynch, Jayson},
  title =	{{Pushing Blocks via Checkable Gadgets: PSPACE-Completeness of Push-1F and Block/Box Dude}},
  booktitle =	{11th International Conference on Fun with Algorithms (FUN 2022)},
  pages =	{3:1--3:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-232-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{226},
  editor =	{Fraigniaud, Pierre and Uno, Yushi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022.3},
  URN =		{urn:nbn:de:0030-drops-159737},
  doi =		{10.4230/LIPIcs.FUN.2022.3},
  annote =	{Keywords: gadgets, motion planning, hardness of games}
}
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