The current study aims to establish a connection between graphs and automata theory, which apparently demonstrate different mathematical structures. Through searching out some properties of one of these structures, we try to find some new properties of the other structure as well. This will result in obtaining some unknown properties. At first, a novel automaton called zero-forcing (Z-F) finite automata is defined 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-finite automata will be obtained. In addition, the language and the closure properties of Z-F-finite 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-finite automata are presented. Further, it is shown that there is not any finite graph such that f be a part of the language of its Z-F-finite automata. Actually, it is proved that for every given graph, the Z-F-finite 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-finite automata of it has a weak closed trail containing all edges. Some examples are also given to clarify these new notions. تفاصيل المقالة

The current study aims to introduce the notions of intuitionistic fuzzy multiset finite automata (IFMFA) concerning a given IFMFA M with states Q. For a subset T of Q, we present the notion of intuitionistic fuzzy multiset submachine generated by T. Furthermore, the behavior of IFMFA is studied and explicated by using algebraic techniques. Further, it is shown that the union and the intersection of a family of an IFMFSA are IFMFSA, as well. Subsequently, it is proved that if IFMFA M has a basis, then the cardinality of the basis is unique. Moreover, the language of IFMFA is examined and some theorems are suggested. تفاصيل المقالة