In [7], Jan Černý conjectured that an arbitrary directable automaton with n states has a directing word of length not longer than (n−1). This conjecture is one of the most longstanding open problems in the theory of finite automata. Most of papers dealing with this conjecture reduce the problem to special classes of automata. In present paper we deal with this conjecture in the class of automat...

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...

A deterministic finite automaton in which every non-empty set of states occurs as the image whole state under action a suitable input word is called completely reachable. We characterize such automata terms graphs and trees.

The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, i...

In [7], a new version of Brzozowski’s algorithm was put forward which relies on regular expression hashing to possibly decrease the number of states in the generated finite state automata. This method utilizes a hash function to decide which states are merged, but does not, in general, construct *-equivalence classes on automaton states, as is done in minimization algorithms. The consequences o...

The partial derivative automaton (Apd) is usually smaller than other non-deterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptoti...

{deniserp, cechin}@exatas.unisinos.br Abstract. This paper presents the use of Recurrent Neural Networks (RNNs) to learn the behavior of the nonlinear dynamic system Inverted Pendulum with a controller and, from the trained neural network, to extract the states of the finite automaton representing the knowledge learned by the neural network. Neural networks store in their weights the knowledge,...

Final task for the course Data Mining, BISS 2006, prof.sa Rosa Meo. 1 Stochastic Finite State Automata (SFSA) In this section we analyse the Hidden Markov Models (HMM) as part of a larger theory, the automata theory, as suggested in [2]. This allows us to show on one hand the relations between these models and others which are well-known pointing out similar and different aspects, on the other ...

Given a timed automaton G accepting the timed language L a finite state machine G 0 can be constructed, known as the region automaton, which accepts the untimed language Untime (L). In this paper we construct an alternative finite state machine which also accepts the language Untime (L), but has fewer states than G 0. This is shown for languages of both finite and infinite traces given that the...

An efficient data structure for representing the full index of a set of strings is the factor automaton, the minimal deterministic automaton representing the set of all factors or substrings of these strings. This paper presents a novel analysis of the size of the factor automaton of an automaton, that is the minimal deterministic automaton accepting the set of factors of a finite set of string...