This paper is a survey on the universal automaton, which is an automaton canonically associated with every language. In the last forty years, many objects have been defined or studied, that are indeed closely related to the universal automaton. We first show that every automaton that accepts a given language has a morphic image which is a subautomaton of the universal automaton of this language...

Left-discrimination of a semigroup is defined and shown to be a sufficient condition that a semigroup be isomorphic to the input semigroup of its semigroup automaton, a necessary condition if the semigroup is finite. The left-discrimination sequence of an automaton is defined as a sequence of semigroups beginning with the input semigroup of the automaton, each member being the input semigroup o...

We present a new self-reproducing cellular automaton capable of construction and computation beyond self-reproduction. Our automaton makes use of some of the concepts developed by Langton for his self-reproducing automaton, but provides the added advantage of being able to perform independent constructional and computational tasks alongside self-reproduction. Our automaton is capable, like Lang...

In this paper, at first, we define the notion of general fuzzy automaton over a field; call vector (VGFA). Moreover, present concept max-min automaton. We show that if two VGFA are similar, they constitute an isomorphism. After that, prove isomorphism with threshold α, equivalent where $\alpha \in [0,1]$. Also, some examples given to clarify these new notions.

Applying formal methods to a group of agents provides a precise and unambiguous definition of their behaviors, as well as verify properties of agents against implementations. Hybrid automaton is one of the formal approaches that are used by several works to model a group of agents. Several logics have been proposed, as extension of temporal logics to specify and hence verify those quantitative ...

We consider cellular automata on Cayley graphs and compare their computational powers according to the architecture on which t h e y work. We show that, if there exists a homomorphism with a nite kernel from a group into another one such that the image of the rst group has a nite index in the second one, then every cellular automaton on the Cayley graph of one of these groups can be uni-formall...