Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton semigroup. We also show that the class of automaton semigroups is closed under the combined operation of ‘free product followed by adjoining an identity’. W...

We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...

In this paper we proposed a Cellular Automaton based local algorithm to solve the autonomously sensor gathering problem in Mobile Wireless Sensor Networks (MWSN). In this problem initially the connected mobile sensors deployed in the network and goal is gather all sensors into one location. The sensors decide to move only based on their local information. Cellular Automaton (CA) as dynamical sy...

We prove that a group G is locally finite if and only if every surjective real (or complex) linear cellular automaton with finite-dimensional alphabet over G is injective.

In previous work, we demonstrated an algorithm that treats a group of robots as a 1-dimensional cellular automaton, which is able to establish formations defined by a single mathematical function. We now extend the algorithm to establish grid formations.

We present a personal perspective, inspired by our own research experience, of the interaction between group theory and automata theory: from Benois’ Theorem to Stallings’ automata, from hyperbolic to automatic groups, not forgetting the exotic automaton groups.

In this paper we characterize when a Cayley automaton semigroup is a group, is trivial, is finite, is free, is a left zero semigroup, or is a right zero semigroup.