Cellular automata are simple models of computation which exhibit fascinatingly complex
behavior. They have captured the attention of several generations of researchers, leading to …

Roughly speaking, the family of combinatorial games consists of two-player games with
perfect information (no hidden information as in some card games), no chance moves (no …

In the past, Cellular Automata based models and machines [1] have been proposed for
simulation of physical systems without any analytical insight into the behaviour of the …

On Nori’s Fundamental Group Scheme Page 1 Progress in Mathematics, Vol. 265, 377–398
c© 2007 Birkhäuser Verlag Basel/Switzerland On Nori’s Fundamental Group Scheme Hél`ene …

A σ-automaton is an additive, binary cellular automaton on a graph. For product graphs such
as a grids and cylinders, reversibility and periodicity properties of the corresponding σ …

We answer some questions concerning the so-called σ-game of Sutner [Linear cellular
automata and the Garden of Eden, Math. Intelligencer11 (1989), 49–53]. It is played on a …

Using number theory on function fields and algebraic number fields, we prove results about
Chebyshev polynomials over finite prime fields to investigate reversibility of two-dimensional …

Lights Out! is an electrical game played on a 5× 5-grid where each cell has a button and an
indicator light. Pressing the button will change the light of the cell and the lights of its …

In this article we study σ (σ+)-automata on finite multidimensional grids with different
boundary conditions. We obtain a natural representation of the global linear map of such …

Let T be a tree with ℓ leaves. Each vertex of T is assigned a state either lit or off. An
assignment of states to all the vertices of T is called a configuration. The lit-only σ-game …