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Documents authored by Hendrickson, Della

Document
DOI: 10.4230/LIPIcs.FUN.2024.1
Baba Is Universal

Authors: Zachary Abel and Della Hendrickson

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

Abstract
We consider the computational complexity of constant-area levels of games which allow an unlimited number of objects in a fixed region. We discuss how to prove that such games are RE-hard (and in particular undecidable) and capable of universal computation, even on constant-area levels. We use the puzzle game Baba is You as a case study, showing that 8×17 levels are capable of universal computation by constructing a particular small universal counter machine within Baba is You.
Cite as

Zachary Abel and Della Hendrickson. Baba Is Universal. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abel_et_al:LIPIcs.FUN.2024.1,
  author =	{Abel, Zachary and Hendrickson, Della},
  title =	{{Baba Is Universal}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{1:1--1:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.1},
  URN =		{urn:nbn:de:0030-drops-199093},
  doi =		{10.4230/LIPIcs.FUN.2024.1},
  annote =	{Keywords: Undecidability, Baba is You, RE-hardness, counter machines, universal computation}
}
Document
DOI: 10.4230/LIPIcs.FUN.2024.23
ASP-Completeness of Hamiltonicity in Grid Graphs, with Applications to Loop Puzzles

Authors: MIT Hardness Group, Josh Brunner, Lily Chung, Erik D. Demaine, Della Hendrickson, and Andy Tockman

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

Abstract
We prove that Hamiltonicity in maximum-degree-3 grid graphs (directed or undirected) is ASP-complete, i.e., it has a parsimonious reduction from every NP search problem (including a polynomial-time bijection between solutions). As a consequence, given k Hamiltonian cycles, it is NP-complete to find another; and counting Hamiltonian cycles is #P-complete. If we require the grid graph’s vertices to form a full m × n rectangle, then we show that Hamiltonicity remains ASP-complete if the edges are directed or if we allow removing some edges (whereas including all undirected edges is known to be easy). These results enable us to develop a stronger "T-metacell" framework for proving ASP-completeness of rectangular puzzles, which requires building just a single gadget representing a degree-3 grid-graph vertex. We apply this general theory to prove ASP-completeness of 37 pencil-and-paper puzzles where the goal is to draw a loop subject to given constraints: Slalom, Onsen-meguri, Mejilink, Detour, Tapa-Like Loop, Kouchoku, Icelom; Masyu, Yajilin, Nagareru, Castle Wall, Moon or Sun, Country Road, Geradeweg, Maxi Loop, Mid-loop, Balance Loop, Simple Loop, Haisu, Reflect Link, Linesweeper; Vertex/Touch Slitherlink, Dotchi-Loop, Ovotovata, Building Walk, Rail Pool, Disorderly Loop, Ant Mill, Koburin, Mukkonn Enn, Rassi Silai, (Crossing) Ichimaga, Tapa, Canal View, and Aqre. The last 13 of these puzzles were not even known to be NP-hard. Along the way, we prove ASP-completeness of some simple forms of Tree-Residue Vertex-Breaking (TRVB), including planar multigraphs with degree-6 breakable vertices, or with degree-4 breakable and degree-1 unbreakable vertices.
Cite as

MIT Hardness Group, Josh Brunner, Lily Chung, Erik D. Demaine, Della Hendrickson, and Andy Tockman. ASP-Completeness of Hamiltonicity in Grid Graphs, with Applications to Loop Puzzles. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mithardnessgroup_et_al:LIPIcs.FUN.2024.23,
  author =	{MIT Hardness Group and Brunner, Josh and Chung, Lily and Demaine, Erik D. and Hendrickson, Della and Tockman, Andy},
  title =	{{ASP-Completeness of Hamiltonicity in Grid Graphs, with Applications to Loop Puzzles}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.23},
  URN =		{urn:nbn:de:0030-drops-199314},
  doi =		{10.4230/LIPIcs.FUN.2024.23},
  annote =	{Keywords: pencil-and-paper puzzles, computational complexity, parsimony}
}
Document
DOI: 10.4230/LIPIcs.FUN.2024.25
Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants

Authors: MIT Hardness Group, Della Hendrickson, and Andy Tockman

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

Abstract
We study three problems related to the computational complexity of the popular game Minesweeper. The first is consistency: given a set of clues, is there any arrangement of mines that satisfies it? This problem has been known to be NP-complete since 2000 [Kaye, 2000], but our framework proves it as a side effect. The second is inference: given a set of clues, is there any cell that the player can prove is safe? The coNP-completeness of this problem has been in the literature since 2011 [Scott et al., 2011], but we discovered a flaw that we believe is present in all published results, and we provide a fixed proof. Finally, the third is solvability: given the full state of a Minesweeper game, can the player win the game by safely clicking all non-mine cells? This problem has not yet been studied, and we prove that it is coNP-complete.
Cite as

MIT Hardness Group, Della Hendrickson, and Andy Tockman. Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mithardnessgroup_et_al:LIPIcs.FUN.2024.25,
  author =	{MIT Hardness Group and Hendrickson, Della and Tockman, Andy},
  title =	{{Complexity of Planar Graph Orientation Consistency, Promise-Inference, and Uniqueness, with Applications to Minesweeper Variants}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.25},
  URN =		{urn:nbn:de:0030-drops-199335},
  doi =		{10.4230/LIPIcs.FUN.2024.25},
  annote =	{Keywords: NP, coNP, hardness, minesweeper, solvability, gadgets, simulation}
}
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