Publications (13)
Pushing Blocks without Fixed Walls via Checkable Gizmos: Push-1 is PSPACE-Complete
MIT Hardness Group, Josh Brunner, Lily Chung +4
We prove PSPACE-completeness of Push-1: given a rectangular grid of 1 x 1 cells, each possibly occupied by a movable block, can a robot move from one specified location to another,…
Complexity of Solo Chess with Unlimited Moves
Josh Brunner, Lily Chung, Michael Coulombe +3
We analyze Solo Chess puzzles, where the input is an board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves…
ASP-Completeness of Hamiltonicity in Grid Graphs, with Applications to Loop Puzzles
MIT Hardness Group, Josh Brunner, Lily Chung +4
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…
Complexity of Retrograde and Helpmate Chess Problems: Even Cooperative Chess is Hard
Josh Brunner, Erik D. Demaine, Dylan Hendrickson +1
We prove PSPACE-completeness of two classic types of Chess problems when generalized to n-by-n boards. A "retrograde" problem asks whether it is possible for a position to be reach…
Complexity of Simple Folding of Mixed Orthogonal Crease Patterns
Hugo Akitaya, Josh Brunner, Erik D. Demaine +3
Continuing results from JCDCGGG 2016 and 2017, we solve several new cases of the simple foldability problem -- deciding which crease patterns can be folded flat by a sequence of (s…
Reconfiguration Algorithms for Cubic Modular Robots with Realistic Movement Constraints
NASA Space Robots Team, Josh Brunner, Kenneth C. Cheung +5
We introduce and analyze a model for self-reconfigurable robots made up of unit-cube modules. Compared to past models, our model aims to newly capture two important practical aspec…
1 x 1 Rush Hour with Fixed Blocks is PSPACE-complete
Josh Brunner, Lily Chung, Erik D. Demaine +4
Consider unit-square blocks in an square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable -- a variat…
An Optimal Algorithm for Online Freeze-tag
Josh Brunner, Julian Wellman
In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and…
Orthogonal Fold & Cut
Hayashi Ani, Josh Brunner, Erik D. Demaine +4
We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then…
Complexity of Reconfiguration in Surface Chemical Reaction Networks
Robert M. Alaniz, Josh Brunner, Michael Coulombe +9
We analyze the computational complexity of basic reconfiguration problems for the recently introduced surface Chemical Reaction Networks (sCRNs), where ordered pairs of adjacent sp…
Arithmetic Expression Construction
Leo Alcock, Sualeh Asif, Jeffrey Bosboom +10
When can given numbers be combined using arithmetic operators from a given subset of to obtain a given target number? We study three variations of this p…
Tetris is Hard with Just One Piece Type
MIT Hardness Group, Josh Brunner, Erik D. Demaine +2
We analyze the computational complexity of Tetris clearing (determining whether the player can clear an initial board using a given sequence of pieces) and survival (determining wh…
The Legend of Zelda: The Complexity of Mechanics
Jeffrey Bosboom, Josh Brunner, Michael Coulombe +4
We analyze some of the many game mechanics available to Link in the classic Legend of Zelda series of video games. In each case, we prove that the generalized game with that mechan…