We give a positive solution to the so-called finite substitution problem which was open for more than 10 years [11]: given recognizable languages K and L, decide whether there exists a finite substitution σ such that σ(K) = L. For this, we introduce a new model of weighted automata and show the decidability of its limitedness problem by solving the underlying Burnside problem.

the aim of this paper is to introduce and study a new concept of strong double δ ( a ) σ -convergence sequences with respect to an orlicz function, and some properties of the resulting sequencespaces were also examined. in addition, we define the δ ( a ) σ -statistical convergence and establish someconnections between the spaces of strong double δ ( a ) σ -convergence sequences and the space of...

Let P(Σ∗) be the semiring of languages, and consider its subset P(Σ). In this paper we define the language recognized by a weighted automaton over P(Σ) and a one-letter alphabet. Similarly, we introduce the notion of language recognition by linear recurrence equations with coefficients in P(Σ). As we will see, these two definitions coincide. We prove that the languages recognized by linear recu...

lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.

In this paper we describe algorithms for finding regularities in weighted sequences. A weighted sequence is a sequence of symbols drawn from an alphabet Σ that have a prespecified probability of occurrence. We show that known algorithms for finding repeats in solid sequences may fail to do so for weighted sequences. In particular, we show that Crochemore’s algorithm for finding repetitions cann...

Let S be a complete star-omega semiring and Σ be an alphabet. For a weighted ω-pushdown automaton P with stateset {1, . . . ,n}, n ≥ 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S≪ Σ ≫),(S≪ Σ ≫)) such that the behavior ‖P‖ of P is a component of a solution of this system. In case the basic semiring is B or N we show that there exists a mixed c...

The theory of two-dimensional languages as a generalization of formal string languages was motivated by problems arising from image processing and pattern recognition and also concerns models of parallel computing. In the nineties, Restivo and Giammarresi defined the family REC of recognizable picture languages [GR97]. This family is very robust and has been characterized by many different devi...

Let S be a complete star-omega semiring and Σ be an alphabet. For a weighted ω-pushdown automaton P with stateset {1, . . . ,n}, n ≥ 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S≪ Σ ≫),(S≪ Σ ≫)) such that the behavior ‖P‖ of P is a component of a solution of this system. In case the basic semiring is B or N we show that there exists a mixed c...