Edoardo Carta-Gerardino

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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)
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)
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)
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