A Kleene Theorem for Weighted Tree Automata

Authors:
Manfred Droste;Christian Pech;Heiko Vogler
Affiliations:
Department of Mathematics and Computer Science, University of Leipzig, D-04109 Leipzig, Germany;Department of Mathematics and Natural Sciences, Dresden University of Technology, D-01062 Dresden, Germany;Department of Computer Science, Dresden University of Technology, D-01062 Dresden, Germany
Venue:
Theory of Computing Systems
Year:
2005

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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.