A Survey of the Game “Lights Out!”

Fleischer, Rudolf; Yu, Jiajin

doi:10.1007/978-3-642-40273-9_13

Cited by 13 publications

(7 citation statements)

References 34 publications

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“…Another problem which was shown in [6] and [9] (and the references therein) to be NP-hard is to determine the minimal number of steps to turn off all lights when you start with all lights on.…”

Section: Lemma 20 the Symmetric Nearest Codeword Problem Is Np-completementioning

confidence: 99%

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Lights Out on graphs

2021

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We model the Lights Out game on general simple graphs in the framework of linear algebra over the field $$\mathbb{F}_{2}$$ F 2 . Based upon a version of the Fredholm alternative, we introduce a separating invariant of the game, i.e., an initial state can be transformed into a final state if and only if the values of the invariant of both states agree. We also investigate certain states with particularly interesting properties. Apart from the classical version of the game, we propose several variants, in particular a version with more than only two states (light on, light off), where the analysis relies on systems of linear equations over the ring $$\mathbb{Z}_{n}$$ Z n . Although it is easy to find a concrete solution of the Lights Out problem, we show that it is NP-hard to find a minimal solution. We also propose electric circuit diagrams to actually realize the Lights Out game.

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Section: Lemma 20 the Symmetric Nearest Codeword Problem Is Np-completementioning

confidence: 99%

“…In particular, conditions are formulated for this particular situation which imply that every initial configuration of lights can be turned off. For a wide historical review of the game and its variants we refer to [9] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Lights Out on graphs

2021

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“…• two variations of the Lights-out puzzle game [Fleischer and Yu, 2013], which consists of a 4 by 4 grid of lights that can be turned on and off, and which starts with a random number of lights initially on-toggling any of the lights also toggles every adjacent light-the objective is to turn every light off;…”

Section: Datasetsmentioning

confidence: 99%

Goal Recognition in Latent Space

Amado

Pereira

Aires

et al. 2018

2018 International Joint Conference on Neural Networks (IJCNN)

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Approaches to goal recognition have progressively relaxed the requirements about the amount of domain knowledge and available observations, yielding accurate and efficient algorithms capable of recognizing goals. However, to recognize goals in raw data, recent approaches require either human engineered domain knowledge, or samples of behavior that account for almost all actions being observed to infer possible goals. This is clearly too strong a requirement for real-world applications of goal recognition, and we develop an approach that leverages advances in recurrent neural networks to perform goal recognition as a classification task, using encoded plan traces for training. We empirically evaluate our approach against the state-of-the-art in goal recognition with image-based domains, and discuss under which conditions our approach is superior to previous ones.

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“…If there exists an activation pattern P which turns all lights off for a given initial configuration C, then the configuration C is called solvable and P is called a solving pattern for C (we may also say P solves C). If every configuration is solvable, then the graph G is called always solvable (it is also called all parity realizable, always winnable, universally solvable by other authors [2], [12], [11]).…”

Section: Introductionmentioning

confidence: 99%

A characterization of always solvable trees in Lights Out game using the activation numbers of vertices

Batal

2020

Preprint

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Lights out is a game that can be played on any simple graph G. A configuration assigns one of the two states on or off to each vertex. For a given configuration, the aim of the game is to turn all vertices off by applying a push pattern on vertices, where each push switches the state of the vertex and its neighbors. If every configuration of vertices is solvable, then we say that the graph is always solvable. We introduce a concept which we call the activation numbers of vertices and we prove several characterization results of graphs by using this concept. We show that for every always solvable graph there exists a chain of always solvable subgraphs where each subgraph differs from the preceding one by a vertex. We also characterize always solvable trees by showing that all always solvable trees can be constructed from always solvable subtrees by some special types of connections. We call the dimension of the space of null-patterns, which leave configurations unchanged, the nullity of the graph G. We show that the nullity of a tree can be characterized by the cardinality of its minimal partition into always solvable subtrees.

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A Survey of the Game “Lights Out!”

Cited by 13 publications

References 34 publications

Lights Out on graphs

Lights Out on graphs

Goal Recognition in Latent Space

A characterization of always solvable trees in Lights Out game using the activation numbers of vertices

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