A word w is called synchronizing (recurrent, reset, magic, directable) word of deterministic nite automaton (DFA) if w sends all states of the automaton to a unique state. In 1964 Jan Cerny found a sequence of n-state complete DFA possessing a minimal synchronizing word of length (n 1)2. He conjectured that it is an upper bound on the length of such words for complete DFA. Nevertheless, the bes...

In this paper, we define the notion of biRFSA which is a residual finate state automaton (RFSA) whose the reverse is also an RFSA. The languages recognized by such automata are called biRFSA languages. We prove that the canonical RFSA of a biRFSA language is a minimal NFA for this language and that each minimal NFA for this language is a sub-automaton of the canonical RFSA. This leads to a char...

For numeration systems representing real numbers and integers, which are based on Pisot numbers, we study expansions with signed digits which are minimal with respect to the absolute sum of digits. It is proved that these expansions are recognizable by a finite automaton if the base β is the root of a polynomial whose (integer) coefficients satisfy a certain condition (D). When β is the Golden ...

We study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. We prove that, for any d > 0, the probability that this number of states is greater than n tends to 1 as n tends to infinity. As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for ...

We study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. We prove that, for any d > 0, the probability that this number of states is greater than n tends to 1 as n tends to infinity. As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for ...

Rauzy graphs of subshifts are endowed with an automaton structure. For Sturmian subshifts, it is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton. A projective limit of the partial semigroups of nonzero regular elements of their transition semigroups is described. If the subshift is minimal, then this projective limit is isomorphic, as a...

In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite state automata and transducers. Traditional methods consist of two steps. The first one is to construct atrie, the second one -to perform minimization. Our approach is to construct an automaton in a single step by adding new strings one by one and minimizing the resulting automaton on-the-fly. We pre...

The 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...

We show that under certain conditions, a language model can be trained on the basis of a second language model. The main instance of the technique trains a finite automaton on the basis of a probabilistic context-free grammar, such that the Kullback-Leibler distance between grammar and trained automaton is provably minimal. This is a substantial generalization of an existing algorithm to train ...

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...