A Kleene Theorem for Weighted Tree Automata |
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| Authors: | Manfred Droste Christian Pech Heiko Vogler |
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| Affiliation: | (1) Department of Mathematics and Computer Science, University of Leipzig, D-04109 Leipzig, Germany;(2) Department of Mathematics and Natural Sciences, Dresden University of Technology, D-01062 Dresden, Germany;(3) Department of Computer Science, Dresden University of Technology, D-01062 Dresden, Germany |
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| Abstract: | In this paper we prove Kleene s result for formal tree series over a commutative semiring A (which is not necessarily complete or continuous or idempotent), i.e., the class of formal tree series over A which are accepted by weighted tree automata, and the class of rational tree series over A are equal. We show the result by direct automata-theoretic constructions and prove their correctness. |
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