相关论文: Solving a Rubik's Cube Using its Local Graph Struc…
The Rubiks Cube, with its vast state space and sparse reward structure, presents a significant challenge for reinforcement learning (RL) due to the difficulty of reaching rewarded states. Previous research addressed this by propagating…
Rubik's Cube is one of the most famous combinatorial puzzles involving nearly $4.3 \times 10^{19}$ possible configurations. Its mathematical description is expressed by the Rubik's group, whose elements define how its layers rotate. We…
The Rubik's cube is a famous puzzle in which faces can be moved and the corresponding movement operations define a group. We consider here a generalization to any $3$-valent map. We prove an upper bound on the size of the corresponding…
This work describes in detail how to learn and solve the Rubik's cube game (or puzzle) in the General Board Game (GBG) learning and playing framework. We cover the cube sizes 2x2x2 and 3x3x3. We describe in detail the cube's state…
Rubik's Revenge, a 4x4x4 variant of the Rubik's puzzles, remains to date as an unsolved puzzle. That is to say, we do not have a method or successful categorization to optimally solve every one of its approximately $7.401 \times 10^{45}$…
The Rubik's Cube is perhaps the world's most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik's Cube also has a rich underlying algorithmic…
Since its first appearance, transformers have been successfully used in wide ranging domains from computer vision to natural language processing. Application of transformers in Reinforcement Learning by reformulating it as a sequence…
Existing combinatorial search methods are often complex and require some level of expertise. This work introduces a simple and efficient deep learning method for solving combinatorial problems with a predefined goal, represented by Rubik's…
Learning to solve a Rubik's Cube requires the learners to repeatedly practice a skill component, e.g., identifying a misplaced square and putting it back. However, for 3D physical tasks such as this, generating sufficient repeated practice…
How many moves does it take to solve Rubik's Cube? Positions are known that require 20 moves, and it has already been shown that there are no positions that require 27 or more moves; this is a surprisingly large gap. This paper describes a…
The paper proposes a novel machine learning-based approach to the pathfinding problem on extremely large graphs. This method leverages diffusion distance estimation via a neural network and uses beam search for pathfinding. We demonstrate…
The core mechanical system is built around three stepper motors for physical manipulation, a microcontroller for hardware control, a camera and YOLO detection model for real-time cube state detection. A significant software component is the…
The first 2x2x2 twisty cube was created as a demonstration tool by Erno Rubik in 1974 to help his students understand the complexity of space and the movements in 3D. He fabricated a novel 3x3x3 mechanism where the 26 cubies were turning,…
We demonstrate that models trained only in simulation can be used to solve a manipulation problem of unprecedented complexity on a real robot. This is made possible by two key components: a novel algorithm, which we call automatic domain…
Rubik's Cube (RC) is a well-known and computationally challenging puzzle that has motivated AI researchers to explore efficient alternative representations and problem-solving methods. The ideal situation for planning here is that a problem…
A generally intelligent agent must be able to teach itself how to solve problems in complex domains with minimal human supervision. Recently, deep reinforcement learning algorithms combined with self-play have achieved superhuman…
A cube is an 8-rep-tile: it is the union of eight smaller copies of itself. Is there a set with a hole which has this property? The computer found an interesting and complicated solution, which then could be simplified. We discuss some…
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
The Sudoku puzzle has achieved worldwide popularity recently, and attracted great attention of the computational intelligence community. Sudoku is always considered as Satisfiability Problem or Constraint Satisfaction Problem. In this…
It is well-known by now that any state of the $3\times 3 \times 3$ Rubik's Cube can be solved in at most 20 moves, a result often referred to as "God's Number". However, this result took Rokicki et al. around 35 CPU years to prove and is…