Cost automata have a finite set of counters which can be manipulated on each transition but do not affect control flow. Based on the evolution of the counter values, these automata define functions from a domain like words or trees to N ∪ {∞}, modulo an equivalence relation which ignores exact values but preserves boundedness properties. These automata have been studied by Colcombet et al. as p...

There are different ways of measuring the complexity of functions that map words to words. Well-known measures are time and space complexity. Enumerability is another possible measure. It is used in recursion theory, where it plays a key rôle in bounded query theory, but also in resource-bounded complexity theory, especially in connection with nonuniform computations. This dissertation transfer...

he purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and ...

Abs t rac t . Two different formalisms for concurrency are compared and are shown to have common foundations. The Input/Output automaton model and the theory of testing are analyzed in the framework of transition systems. The relationship between the fair and quiescent preorders of I/O automata is investigated and the two preorders are shown to coincide on a large class of automata. I/O automat...

Two diierent formalisms for concurrency are compared and are shown to have common foundations. The Input/Output automaton model and the theory of testing are analyzed in the framework of transition systems. The relationship between the fair and quiescent preorders of I/O automata is investigated and the two preorders are shown to coincide on a large class of automata. I/O automata are encoded i...

The objective of this survey is to present the ideal theory of monoids, the so-called Green’s relations, and to illustrate the usefulness of this tool for solving automata related questions. We use Green’s relations for proving four classical results related to automata theory: The result of Schützenberger characterizing star-free languages, the theorem of factorization forests of Simon, the ch...

The general theory of randomly timed automata is developed: starting with the practical motivation and presentation of the envisaged notion, the categorical theory of minimization, aggregation, encapsulation, interconnection and realization of such automata is worked out. All these constructions are presented universally: minimization and realization as adjunctions, aggregation as product, inte...

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...