In this paper, the concepts of somewhat fuzzy Automata continuous functions and somewhat fuzzy Automata open functions in fuzzy Automata topological spaces are introduced and some interesting properties of these functions are studied. In this connection, the concepts of fuzzy Automata resolvable spaces and fuzzy Automata irresolvable spaces are also introduced and their properties are studied.

The current study aims to establish a connection between graphs and Automata theory, which apparently demonstrate di erent mathematical structures. Through searching out some properties of one of these structures, we try to  nd some new properties of the other structure as well. This will result in obtaining some unknown properties. At  rst, a novel automaton called zero-forcing (Z-F)  nite Automata is de ned according to the notion of a zero-forcing set of a graph. It is shown that for a given graph and for some zero forcing sets, various Z-F- nite Automata will be obtained. In addition, the language and the closure properties of Z-F- nite Automata, in particular; union, connection, and serial connection are studied. Moreover, considering some properties of graphs such as the closed trail, connected and complete; some new features for Z-F- nite Automata are presented. Further, it is shown that there is not any  nite graph such that f be a part of the language of its Z-F- nite Automata. Actually, it is proved that for every given graph, the Z-F- nite Automata of it does not show any closed trail containing all edges for every zero forcing set, but if the graph G has been a closed trail containing all edges, then the Z-F- nite Automata of it has a weak closed trail containing all edges. Some examples are also given to clarify these new notions.

In this paper, the authors have represented the genetic structures in terms of Automata. With the algebraic structure defined on the genetic code authors defined an automaton on those codons as Σ,= (CG, P, AM, F, G) where P is the set of the four bases A, C, G, U as a set of alphabets or inputs, CG is the set of all 64 codons, obtained from the ordering of the elements of P, as the set of states, AM is the set of the 20 amino acids as the set of outputs that produce during the process. F and G are transition function and output function respectively. Authors observed that M(Σ, ) = ({fa: a ∈,P}, ◦, ) defined on the Automata Σ,where fa(q) = F(q, a) = qa, q ∈,CG, a ∈,P is a monoid called the syntactic monoid of Σ, , with fa ◦,fb = fba ∀, a, b ∈,P. Studying the structure defined in terms of Automata it is also observed that the algebraic structure (M(CG), +, ·, ) forms a Near-Ring with respect to the two operations ′,+ ′,and ′, ·, ′,where M(CG) = {f|f: CG →,CG}.

In this paper, we define the notion of a bipolar general fuzzy automaton, then we construct some closure operators on the set of states of a bipolar general fuzzy automaton. Also, we construct some topologies on the set of states of a bipolar general fuzzy automaton. Then we obtain some relationships between them.

In this paper, we introduce open cellular learning Automata and then study its convergence behavior. It is shown that for a class of rules called commutative rules, the open cellular learning Automata in stationary external environments converges to a stable and compatible configuration. The numerical results also confirm the theory.  

The aim of this paper is the study of a covering of a max-min general fuzzy automaton by another, admissible relations, admissible partitions of a max-min general fuzzy automaton, d~-orthogonality of admissible partitions, irreducible max-min general fuzzy Automata. Then we obtain the relationships between them.