相关论文: Post-critically finite self-similar groups

We develop a group graded Morita theory over a G-graded G-acted algebra, where G is a finite group.

In the 1980's Stallings showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse…

We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories. We work through numerous examples to demonstrate the power of these notions. Turning to representations, which are actions that…

We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…

We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

In this paper we study the logical aspects of branching automata, as defined by Lodaya and Weil. We first prove that the class of languages of finite N-free posets recognized by branching automata is closed under complementation. Then we…

We introduce the class of tree constraint automata with data values in Z (equipped with the less than relation and equality predicates to constants) and we show that the nonemptiness problem is ExpTime-complete. Using an automata-based…

We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…

A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…

We present a novel form of Liquid Automata, using this to simulate autopoiesis, whereby living machines self-organise in the physical realm. This simulation is based on an earlier Cellular Automaton described by Francisco Varela. The basis…

Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…

In this paper, we study some large scale properties of the mother groups of bounded automata groups. First we give two methods to prove every mother group has infinite asymptotic dimension. Then we study the decomposition complexity of…

The notions of nonpositive curved spaces and biautomatic groups are generalizations of the geometric properties of hyperbolic spaces and computational properties of their fundamental groups. Given the mutual origins of these conditions, one…

A complete deterministic finite automaton in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize completely…

Choreography automata are an automata-based model of choreographies, that we show to be a compositional one. Choreography automata represent global views of choreographies (and rely on the well-known model of communicating finite-state…

Two new classes of finite automata, called General hexagonal Boustrophedon finite automata and General hexagonal returning finite automata operating on hexagonal grids, are introduced and analyzed. The work establishes the theoretical…

Let $A$ be a finite group acting by automorphisms on the finite group $G$. We introduce the commuting graph $\Gamma (G,A)$ of this action and study some questions related to the structure of $G$ under certain graph theoretical conditions on…

The Poisson boundary of a finite direct product of affine automorphism groups of homogeneous trees is considered. The Poisson boundary is shown to be a product of ends of trees with a hitting measure for spread-out, aperiodic measures of…

We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an…