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Documents authored by Bosboom, Jeffrey

Document
DOI: 10.4230/LIPIcs.ISAAC.2020.12
Arithmetic Expression Construction

Authors: Leo Alcock, Sualeh Asif, Jeffrey Bosboom, Josh Brunner, Charlotte Chen, Erik D. Demaine, Rogers Epstein, Adam Hesterberg, Lior Hirschfeld, William Hu, Jayson Lynch, Sarah Scheffler, and Lillian Zhang

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
When can n given numbers be combined using arithmetic operators from a given subset of {+,-,×,÷} to obtain a given target number? We study three variations of this problem of Arithmetic Expression Construction: when the expression (1) is unconstrained; (2) has a specified pattern of parentheses and operators (and only the numbers need to be assigned to blanks); or (3) must match a specified ordering of the numbers (but the operators and parenthesization are free). For each of these variants, and many of the subsets of {+,-,×,÷}, we prove the problem NP-complete, sometimes in the weak sense and sometimes in the strong sense. Most of these proofs make use of a rational function framework which proves equivalence of these problems for values in rational functions with values in positive integers.
Cite as

Leo Alcock, Sualeh Asif, Jeffrey Bosboom, Josh Brunner, Charlotte Chen, Erik D. Demaine, Rogers Epstein, Adam Hesterberg, Lior Hirschfeld, William Hu, Jayson Lynch, Sarah Scheffler, and Lillian Zhang. Arithmetic Expression Construction. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alcock_et_al:LIPIcs.ISAAC.2020.12,
  author =	{Alcock, Leo and Asif, Sualeh and Bosboom, Jeffrey and Brunner, Josh and Chen, Charlotte and Demaine, Erik D. and Epstein, Rogers and Hesterberg, Adam and Hirschfeld, Lior and Hu, William and Lynch, Jayson and Scheffler, Sarah and Zhang, Lillian},
  title =	{{Arithmetic Expression Construction}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.12},
  URN =		{urn:nbn:de:0030-drops-133568},
  doi =		{10.4230/LIPIcs.ISAAC.2020.12},
  annote =	{Keywords: Hardness, algebraic complexity, expression trees}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.1
Tatamibari Is NP-Complete

Authors: Aviv Adler, Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Quanquan C. Liu, and Jayson Lynch

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an m x n grid of cells, where each cell possibly contains a clue among ⊞, ⊟, ◫. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exactly one clue, rectangles containing ⊞ are square, rectangles containing ⊟ are strictly longer horizontally than vertically, rectangles containing ◫ are strictly longer vertically than horizontally, and no four rectangles share a corner. We prove this puzzle NP-complete, establishing a Nikoli gap of 16 years. Along the way, we introduce a gadget framework for proving hardness of similar puzzles involving area coverage, and show that it applies to an existing NP-hardness proof for Spiral Galaxies. We also present a mathematical puzzle font for Tatamibari.
Cite as

Aviv Adler, Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Quanquan C. Liu, and Jayson Lynch. Tatamibari Is NP-Complete. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{adler_et_al:LIPIcs.FUN.2021.1,
  author =	{Adler, Aviv and Bosboom, Jeffrey and Demaine, Erik D. and Demaine, Martin L. and Liu, Quanquan C. and Lynch, Jayson},
  title =	{{Tatamibari Is NP-Complete}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{1:1--1:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.1},
  URN =		{urn:nbn:de:0030-drops-127624},
  doi =		{10.4230/LIPIcs.FUN.2021.1},
  annote =	{Keywords: Nikoli puzzles, NP-hardness, rectangle covering}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.3
Walking Through Doors Is Hard, Even Without Staircases: Proving PSPACE-Hardness via Planar Assemblies of Door Gadgets

Authors: Joshua Ani, Jeffrey Bosboom, Erik D. Demaine, Yenhenii Diomidov, Dylan Hendrickson, and Jayson Lynch

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
A door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "open" and "close" tunnel sets the gadget’s state to open and closed, respectively, while the "traverse" tunnel can be traversed if and only if the door is in the open state. We prove that it is PSPACE-complete to decide whether an agent can move from one location to another through a planar assembly of such door gadgets, removing the traditional need for crossover gadgets and thereby simplifying past PSPACE-hardness proofs of Lemmings and Nintendo games Super Mario Bros., Legend of Zelda, and Donkey Kong Country. Our result holds in all but one of the possible local planar embedding of the open, close, and traverse tunnels within a door gadget; in the one remaining case, we prove NP-hardness. We also introduce and analyze a simpler type of door gadget, called the self-closing door. This gadget has two states and only two tunnels, similar to the "open" and "traverse" tunnels of doors, except that traversing the traverse tunnel also closes the door. In a variant called the symmetric self-closing door, the "open" tunnel can be traversed if and only if the door is closed. We prove that it is PSPACE-complete to decide whether an agent can move from one location to another through a planar assembly of either type of self-closing door. Then we apply this framework to prove new PSPACE-hardness results for several 3D Mario games and Sokobond.
Cite as

Joshua Ani, Jeffrey Bosboom, Erik D. Demaine, Yenhenii Diomidov, Dylan Hendrickson, and Jayson Lynch. Walking Through Doors Is Hard, Even Without Staircases: Proving PSPACE-Hardness via Planar Assemblies of Door Gadgets. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ani_et_al:LIPIcs.FUN.2021.3,
  author =	{Ani, Joshua and Bosboom, Jeffrey and Demaine, Erik D. and Diomidov, Yenhenii and Hendrickson, Dylan and Lynch, Jayson},
  title =	{{Walking Through Doors Is Hard, Even Without Staircases: Proving PSPACE-Hardness via Planar Assemblies of Door Gadgets}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.3},
  URN =		{urn:nbn:de:0030-drops-127642},
  doi =		{10.4230/LIPIcs.FUN.2021.3},
  annote =	{Keywords: gadgets, motion planning, hardness of games}
}
Document
DOI: 10.4230/LIPIcs.FUN.2018.3
Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible

Authors: Zachary Abel, Jeffrey Bosboom, Erik D. Demaine, Linus Hamilton, Adam Hesterberg, Justin Kopinsky, Jayson Lynch, and Mikhail Rudoy

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract
We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a path in a rectangular grid graph from a start vertex to a destination vertex. The different puzzle types place different constraints on the path: preventing some edges from being visited (broken edges); forcing some edges or vertices to be visited (hexagons); forcing some cells to have certain numbers of incident path edges (triangles); or forcing the regions formed by the path to be partially monochromatic (squares), have exactly two special cells (stars), or be singly covered by given shapes (polyominoes) and/or negatively counting shapes (antipolyominoes). We show that any one of these clue types (except the first) is enough to make path finding NP-complete ("witnesses exist but are hard to find"), even for rectangular boards. Furthermore, we show that a final clue type (antibody), which necessarily "cancels" the effect of another clue in the same region, makes path finding Sigma_2-complete ("witnesses do not exist"), even with a single antibody (combined with many anti/polyominoes), and the problem gets no harder with many antibodies.
Cite as

Zachary Abel, Jeffrey Bosboom, Erik D. Demaine, Linus Hamilton, Adam Hesterberg, Justin Kopinsky, Jayson Lynch, and Mikhail Rudoy. Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{abel_et_al:LIPIcs.FUN.2018.3,
  author =	{Abel, Zachary and Bosboom, Jeffrey and Demaine, Erik D. and Hamilton, Linus and Hesterberg, Adam and Kopinsky, Justin and Lynch, Jayson and Rudoy, Mikhail},
  title =	{{Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{3:1--3:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.3},
  URN =		{urn:nbn:de:0030-drops-87944},
  doi =		{10.4230/LIPIcs.FUN.2018.3},
  annote =	{Keywords: video games, puzzles, hardness}
}
Document
DOI: 10.4230/LIPIcs.FUN.2018.11
Computational Complexity of Generalized Push Fight

Authors: Jeffrey Bosboom, Erik D. Demaine, and Mikhail Rudoy

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract
We analyze the computational complexity of optimally playing the two-player board game Push Fight, generalized to an arbitrary board and number of pieces. We prove that the game is PSPACE-hard to decide who will win from a given position, even for simple (almost rectangular) hole-free boards. We also analyze the mate-in-1 problem: can the player win in a single turn? One turn in Push Fight consists of up to two "moves" followed by a mandatory "push". With these rules, or generalizing the number of allowed moves to any constant, we show mate-in-1 can be solved in polynomial time. If, however, the number of moves per turn is part of the input, the problem becomes NP-complete. On the other hand, without any limit on the number of moves per turn, the problem becomes polynomially solvable again.
Cite as

Jeffrey Bosboom, Erik D. Demaine, and Mikhail Rudoy. Computational Complexity of Generalized Push Fight. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bosboom_et_al:LIPIcs.FUN.2018.11,
  author =	{Bosboom, Jeffrey and Demaine, Erik D. and Rudoy, Mikhail},
  title =	{{Computational Complexity of Generalized Push Fight}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.11},
  URN =		{urn:nbn:de:0030-drops-88029},
  doi =		{10.4230/LIPIcs.FUN.2018.11},
  annote =	{Keywords: board games, hardness, mate-in-one}
}
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