Related papers: Lights Out on graphs
We study a version of the lights out game played on directed graphs. For a digraph $D$, we begin with a labeling of $V(D)$ with elements of $\mathbb{Z}_k$ for $k \ge 2$. When a vertex $v$ is toggled, the labels of $v$ and any vertex that…
Consider a game played on a simple graph $G = (V, E)$ where each vertex consists of a clickable light. Clicking any vertex $v$ toggles the on/off state of $v$ and its neighbors. Starting from an initial configuration of lights, one wins the…
We answer some questions concerning the so called sigma-game of Sutner. It is played on a graph where each vertex has a lamp, the light of which is toggled by pressing any vertex with an edge directed to the lamp. For example, we show that…
We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (vass) and…
Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model…
We consider games played on graphs with the winning conditions for the players specified as weak-parity conditions. In weak-parity conditions the winner of a play is decided by looking into the set of states appearing in the play, rather…
The notions of captured/lost vertices and dead edges in the Shannon game (Shannon switching game on nodes) are examined using graph theory. Simple methods are presented for identifying some dead edges and some captured sets of vertices,…
With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…
Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…
We consider zero-sum games in which players move between adjacent states, where in each pair of adjacent states one state dominates the other. The states in our game can represent positional advantages in physical conflict such as high…
We propose a method to construct finite-state reactive controllers for systems whose interactions with their adversarial environment are modeled by infinite-duration two-player games over (possibly) infinite graphs. The proposed method…
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to…
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
This survey addresses pluri-periodic harmonic functions on lattices with values in a positive characteristic field. We mention, as a motivation, the game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware,…
Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a "quantum-classical game"--that is, a non-local game of two…
We present the notion of separable game with respect to a forward directed hypergraph (FDH-graph), which refines and generalizes that of graphical game. First, we show that there exists a minimal FDH-graph with respect to which a game is…