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In this paper we investigate tree automata with multiplicities on a semiring and prove that the recognizable treeseries are exactly the projections of local
(
of T
Σ generated from
). Moreover to each treeautomation A over a semiring, we have associated a normalized one A′ whose behaviour coincides with that of A on the set T
Σ − Σ0 (=all trees except the constants).
Finally we solve the emptyness problem for a subset.
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-Treeautomata and their relation to weighted context-free grammars