Does the lit-only restriction make any difference for the σ-game and σ+-game?

Authors:
John Goldwasser;Xinmao Wang;Yaokun Wu
Affiliations:
Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States;Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China;Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China
Venue:
European Journal of Combinatorics
Year:
2009

Citing 15
Cited 3

On characterization of state transition graph of additive cellular automata based on depth

Information Sciences: an International Journal
Reachability is decidable in the numbers game

Theoretical Computer Science
Universal configurations in light-flipping games

SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Note on the Lamp Lighting Problem

Advances in Applied Mathematics
Cellular automata and intermediate reachability problems

Fundamenta Informaticae - Special issue on cellular automata
The Minimum All-Ones Problem for Trees

SIAM Journal on Computing
Chebyshev polynomials over finite fields and reversibility of σ-automata on square grids

Theoretical Computer Science
On irreversibility of von Neumann additive cellular automata on grids

Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Complexity of reachability problems for finite discrete dynamical systems

Journal of Computer and System Sciences
Note: Minimum light number of lit-only σ-game on a tree

Theoretical Computer Science
On the complexity of dominating set problems related to the minimum all-ones problem

Theoretical Computer Science
Linear algebra approach to geometric graphs

Journal of Combinatorial Theory Series A
Eriksson's numbers game and finite Coxeter groups

European Journal of Combinatorics
The general σ all-ones problem for trees

Discrete Applied Mathematics
Lit-only sigma game on a line graph

European Journal of Combinatorics

The edge-flipping group of a graph

European Journal of Combinatorics
Completely symmetric configurations for σ-games on grid graphs

Journal of Algebraic Combinatorics: An International Journal
Lit-only σ-game on pseudo-trees

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Each vertex in a simple graph is in one of two states: "on" or "off". The set of all on vertices is called a configuration. In the σ-game, "pushing" a vertex v changes the state of all vertices in the open neighborhood of v, while in the σ+-game pushing v changes the state of all vertices in its closed neighborhood. The reachability question for these two games is to decide whether a given configuration can be reached from a given starting configuration by a sequence of pushes. We consider the lit-only restriction on these two games where a vertex can be pushed only if it is in the on state. We show that the lit-only restriction can make a big difference for reachability in the σ-game, but has essentially no effect in the σ+-game.