Direct and dual laws for automata with multiplicities

We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities). We show that classical formulas are optimal for the bounds. Especially they are almost everywhere optimal for the fields R and C. We characterize the dual laws preserving rationality and examine compatibility between the geometry of the K-automata andthese laws. Copyright 2001 Elsevier Science B.V.

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