相关论文: Automata, Groups, Limit Spaces, and Tilings
We investigate the action of the automorphism group of a closed Riemann surface on its set of theta characteristics (or spin structures). We give criteria for when an automorphism fixes all spin structures, or when it fixes just one. The…
In this paper we develop a dynamical scaling limit from rational dynamics to automata in tropical geometry. We compare these dynamics and induce uniform estimates of their orbits. We apply these estimates to introduce a comparison analysis…
We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual…
We introduce a new class of semigroups arising from a restricted class of asynchronous automata. We call these semigroups "expanding automaton semigroups." We show that the class of synchronous automaton semigroups is strictly contained in…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
We study the connection between small-overlap conditions and automaticity of semigroups. We restrict the discussion to conditions that imply embeddability and under which each relation decomposes into at least seven pieces. For these…
We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R^n-trees. We first prove that Sela's limit groups do have a free action on an R^n-tree. We then prove that a finitely generated group having…
We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…
In this paper we study the problem of determining the homology groups of a quotient of a topological space by an action of a group. The method is to represent the original topological space as a homotopy limit of a diagram, and then act…
We give a simple proof of the finite presentation of Sela's limit groups by using free actions on $\bbR^n$-trees. We first prove that Sela's limit groups do have a free action on an $\bbR^n$-tree. We then prove that a finitely generated…
We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices that consists in grouping neighboring cells into tiles and selecting a subspace within each tile. This is done in such a way that multiple evolution…
This paper generalizes Bass' work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The…
We organize fundamental properties of quasi-Hamiltonian spaces on which a finite group acts, and we apply them to the theory of moduli spaces of flat connections on an oriented compact surface with boundary.
We consider methods for connected reconfigurations by finite automate in the so-called \emph{hybrid} or \emph{Robot-on-Tiles} model of programmable matter, in which a number of simple robots move on and rearrange an arrangement of passive…
Cellular automata can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schr\"odinger equation together with its conservation laws. Surprisingly, a whole class of…
Tree-graded spaces are generalizations of R-trees. They appear as asymptotic cones of groups (when the cones have cut points). Since many questions about endomorphisms and automorphisms of groups, solving equations over groups, studying…
We develop an effective and natural approach to interpret any semigroup admitting a special language of greedy normal forms as an automaton semigroup,namely the semigroup generated by a Mealy automaton encoding the behaviour of such a…
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…
In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we describe an algorithmic procedure for building a finite…
We devise an algorithm which, given a bounded automaton A, decides whether the group generated by A is finite. The solution comes from a description of the infinite sequences having an infinite A-orbit using a deterministic finite-state…