Automata over a symmetric monoidal category M are introduced, and a multi-step simulation is defined among such automata. The collection of M automata is given the structure of a 2-category on the same objects as M , in which the vertical structure is determined by groups of indistinguishable simulations. TwoM -automata are called simulation equivalent if they are connected by an isomorphism of...

We study the problem of closure under complementation of languages accepted by one-way and two-way tree automata modulo equational theories. We deal with the equational theories of commutative monoids ( ), idempotent commutative monoids ( ), Abelian groups ( ), and the theories of exclusive-or ( ), generalized exclusive-or ( ), and distributive minus symbol ( ). While the one-way automata for a...

We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean closure of the class of deterministic context-free languages while the class of languages accepted by nondeterministic multipass automata is exactly the clas...

We investigate the orbits of automaton semigroups and groups to obtain algorithmic structural results, both for general automata but also some special subclasses. First, we show that a more version finiteness problem is undecidable. This equivalent left principal ideals in generated by complete reversible automata. Then, look at w-word (i.\,e.\ right infinite words) with finite orbit. every yie...

This is an overview of results concerning applications of self-similar groups generated by automata to fractal geometry and dynamical systems. Few proofs are given, interested reader can find the rest of the proofs in the monograph [Nek05]. We associate to every contracting self-similar action a topological space JG called limit space together with a surjective continuous map s : JG −→ JG. On t...

In this paper, a new algorithm which is the result of the combination of cellular learning automata and frog leap algorithm (SFLA) is proposed for optimization in continuous, static environments.At the proposed algorithm, each memeplex of frogs is placed in a cell of cellular learning automata. Learning automata in each cell acts as the brain of memeplex, and will determine the strategy of moti...

In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept. We show how one can decompose an arbitrary regular subset of a finite rank free group into disjoint union of sets accepted by special automata or special monoids. These automata allow us to compute explicitly generating functions, λ−measures and Cesaro meas...

We investigate co-indexed groups, that is groups whose co-word problem (all words defining nontrivial elements) is an indexed language. We show that all Higman-Thompson groups and a large class of tree automorphism groups defined by finite automata are co-indexed groups. The latter class is closely related to dynamical systems and includes the Grigorchuk 2-group and the Gupta-Sidki 3-group. The...