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We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change…

We analyze the computational complexity of motion planning through local "input/output" gadgets with separate entrances and exits, and a subset of allowed traversals from entrances to exits, each of which changes the state of the gadget and…

Push-1 is one of the simplest abstract frameworks for motion planning; however, the complexity of deciding if a Push-1 problem can be solved was a several-decade-old open question. We resolve the complexity of the motion planning problem…

Consider an agent traversing a graph of "gadgets", each with local state that changes with each traversal by the agent. We characterize the complexity of universal traversal, where the goal is to traverse every gadget at least once, for DAG…

We prove PSPACE-completeness of several reversible, fully deterministic systems. At the core, we develop a framework for such proofs (building on a result of Tsukiji and Hagiwara and a framework for motion planning through gadgets), showing…

We prove PSPACE-hardness for fifteen games in the Super Mario Bros. 2D platforming video game series. Previously, only the original Super Mario Bros. was known to be PSPACE-hard (FUN 2016), though several of the games we study were known to…

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, given the ability to push up to one block at a time? In…

We build a general theory for characterizing the computational complexity of motion planning of robot(s) through a graph of "gadgets", where each gadget has its own state defining a set of allowed traversals which in turn modify the…

We prove PSPACE-completeness of the well-studied pushing-block puzzle Push-1F, a theoretical abstraction of many video games (introduced in 1999). The proof also extends to Push-$k$ for any $k \ge 2$. We also prove PSPACE-completeness of…

We prove that a variant of 2048, a popular online puzzle game, is PSPACE-Complete. Our hardness result holds for a version of the problem where the player has oracle access to the computer player's moves. Specifically, we show that for an…

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 mechanic is polynomial, NP-complete, NP-hard and in PSPACE, or…

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of…

We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of…

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…

Bloxorz is an online puzzle game where players move a 1 by 1 by 2 block by tilting it on a subset of the two dimensional grid. Bloxorz features switches that open and close trapdoors. The puzzle is to move the block from its initial…

Using doors is a longstanding challenge in robotics and is of significant practical interest in giving robots greater access to human-centric spaces. The task is challenging due to the need for online adaptation to varying door properties…

Micro- and nanorobots are often controlled by global input signals, such as an electromagnetic or gravitational field. These fields move each robot maximally until it hits a stationary obstacle or another stationary robot. This paper…

We introduce and investigate the computational complexity of a novel physical problem known as the Pinball Wizard problem. It involves an idealized pinball moving through a maze composed of one-way gates (outswing doors), plane walls,…

We show that the Minesweeper game is PP-hard, when the object is to locate all mines with the highest probability. When the probability of locating all mines may be infinitesimal, the Minesweeper game is even PSPACE-complete. In our…

Many puzzle video games, like Sokoban, involve moving some agent in a maze. The reachable locations are usually apparent for a human player, and the difficulty of the game is mainly related to performing actions on objects, such as pushing…