Related papers: Motion planning with pull moves
We are going to show that some variants of a puzzle called Pull in which the boxes have handles (i.e. we can only pull the boxes in certain directions) are NP-hard
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 prove PSPACE-completeness of all but one problem in a large space of pulling-block problems where the goal is for the agent to reach a target destination. The problems are parameterized by whether pulling is optional, the number of…
We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum in-flow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse…
In unlabeled multi-robot motion planning several interchangeable robots operate in a common workspace. The goal is to move the robots to a set of target positions such that each position will be occupied by some robot. In this paper, we…
We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…
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…
Despite significant progress in general AI planning, certain domains remain out of reach of current AI planning systems. Sokoban is a PSPACE-complete planning task and represents one of the hardest domains for current AI planners. Even…
In the problem of multi-robot motion planning, a group of robots, placed in a polygonal domain with obstacles, must be moved from their starting positions to a set of target positions. We consider the specific case of unlabeled disc robots…
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…
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…
We partially reverse-engineer a convolutional recurrent neural network (RNN) trained with model-free reinforcement learning to play the box-pushing game Sokoban. We find that the RNN stores future moves (plans) as activations in particular…
The paper is concerned with the two-machine flow shop, where each job requires an additional resource (referred to as storage space) from the start of its first operation till the end of its second operation. The storage requirement of a…
Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap.…
Planning is essential for solving complex tasks, yet the internal mechanisms underlying planning in neural networks remain poorly understood. Building on prior work, we analyze a recurrent neural network (RNN) trained on Sokoban, a…
An open-close door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "opening" and "closing" tunnels set the gadget's state to open and closed, respectively, while the "traverse" tunnel can…
We show that the problem of finding an optimal stochastic 'blind' controller in a Markov decision process is an NP-hard problem. The corresponding decision problem is NP-hard, in PSPACE, and SQRT-SUM-hard, hence placing it in NP would imply…
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…
The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of…
Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide…