On computational power of weighted finite automata
Weighted Finite Automata are automata with multiplicities used to compute real functions by reading infinite words. We 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 allows to decide whether a function computed by a level automaton is smooth or not.
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