Rational series and their languages
Rational series and their languages
Finite Automata Computing Real Functions
SIAM Journal on Computing
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
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Weighted Finite Automata are automata with multiplicities used to compute real functions by reading infinite words. The aim of this paper is to study what kind of functions can be computed by level automata, a particular subclass of WFA. Several results concerning the continuity and the smoothness of these functions are shown. In particular, the only smooth functions that can be obtained are the polynomials. This enables to decide whether a function computed by a level automaton is smooth or not.