The purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. This is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.

The concept of an automaton group generalizes easily to semigroups, and the systematic study of this area is beginning. This paper aims to contribute to that study. The basic theory of automaton semigroups is briefly reviewed. Various natural semigroups are shown to arise as automaton semigroups. The interaction of certain semigroup constructions with the class of automaton semigroups is studie...

We prove that if the group generated by an invertible and reversible Mealy automaton acts level-transitively on a regular rooted tree, then the semigroup generated by the dual automaton has exponential growth, hence giving a decision procedure of exponential growth for a restricted family of automaton (semi)groups. The purpose of this note is to link up two classes of groups and semigroups high...

We introduce a new tool, called the orbit automaton, that describes the action of an automaton group G on the subtrees corresponding to the orbits of G on levels of the tree. The connection between G and the groups generated by the orbit automata is used to find elements of infinite order in certain automaton groups for which other methods failed to work.

A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be...

A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be...

In this paper, relations among the membership values of gener- alized fuzzy languages such as intuitionistic fuzzy language, interval-valued fuzzy language and vague language are studied. It will aid in studying the properties of one language when the properties of another are known. Further, existence of a minimized nite automaton with vague ( final) states for any vague regular language recog...

We prove that every linear-activity automaton group is amenable. The proof is based on showing that a sufficiently symmetric random walk on a specially constructed degree 1 automaton group — the mother group — has asymptotic entropy 0. Our result answers an open question by Nekrashevich in the Kourovka notebook, and gives a partial answer to a question of Sidki. Figure 1: A Schreier graph for a...

In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton.In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented.It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finall...

Using a cellular automata approach we create models of people movement within buildings. Simple, local update rules capturing the movement of individuals are shown to produce realistic behaviour of crowds, that is, collections of individuals. We demonstrate how distinct crowd behaviour at constriction points is characterised using different update rules. These distinct rules are produced in an ...