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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… (More)

In the last few decades, several techniques to randomly generate a deterministic finite automaton have been developed. These techniques have implications in the enumeration and random generation of automata of size n. One of the ways to generate a finite automaton is to generate a random tree and to complete it to a deterministic finite automaton, assuming… (More)

A nonhomogeneous system of linear recurrence equations can be recognized by an automaton A over a one-letter alphabet A = {z}. Conversely, the automaton A generates precisely this nonhomogeneous system of linear recurrence equations. We present the solutions of these systems and apply the z-transform to these solutions to obtain their series representation.… (More)

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