We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component and the form of any such additional components. Our characterization applies, in particular, to any automaton arising from a Bertrand numeration system. Furthermore, we show th...

In this paper we focus on the construction of the minimal deterministic finite automaton Sk that recognizes the set of suffixes of a word w up to k errors. We present an algorithm that makes use of the automaton Sk in order to accept in an efficient way the language of all suffixes of w up to k errors in every windows of size r, where r is the value of the repetition index of w. Moreover, we gi...

GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from dealing with low-level data structures. In this case study, we present a graph program which minimizes finite automata. The program represents an automaton by its transition diagram, computes the state equivalence relation, and merges...

With every rational language we associate a canonical non-determinis-tic automaton, that subsumes all possible \minimal" automata recognizing this language.

In this paper an attempt has been made to represent biological mutational activities through sequential mathematical machines. Begin with a brief theory of finite state sequential machines genetic sequences are presented in a systematic manner. A mutator has been shown as a variety of finite state machines. The mutation is studied systematically and an automaton have been constructed with the b...

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.

We adapt the Coarsest Partition Reenement algorithm to its computation using the speciic data structures of Binary Decision Diagrams. This allows to generate symbolically the set of equivalence classes of a nite automaton with respect to bisim-ulation, without constructing the automaton itself. These equivalence classes represent of course the (new) states of the canonical minimal automaton bis...

the purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. this is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.

One approach to formally specifying a system is to use a form of extended finite-state machine called a stream X-machine. A stream X-machine is a type of X-machine that describes a system as a finite set of states, each with an internal store, called memory, and a number of transitions between the states. A stream X-machine may be modelled by a finite automaton (the associated finite automaton)...