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A Büchi-Like Theorem for Weighted Tree Automata over Multioperator Monoids

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Abstract

A multioperator monoid \(\mathcal{A}\) is a commutative monoid with additional operations on its carrier set. A weighted tree automaton over \(\mathcal{A}\) is a finite state tree automaton of which each transition is equipped with an operation of \(\mathcal{A}\). We define M-expressions over \(\mathcal{A}\) in the spirit of formulas of weighted monadic second-order logics and, as our main result, we prove that if \(\mathcal{A}\) is absorptive, then the class of tree series recognizable by weighted tree automata over \(\mathcal{A}\) coincides with the class of tree series definable by M-expressions over \(\mathcal{A}\). This result implies the known fact that for the series over semirings recognizability by weighted tree automata is equivalent with definability in syntactically restricted weighted monadic second-order logic. We prove this implication by providing two purely syntactical transformations, from M-expressions into formulas of syntactically restricted weighted monadic second-order logic, and vice versa.

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Authors and Affiliations

  1. Department of Computer Science, University of Szeged, Árpád tér 2., 6720, Szeged, Hungary

    Zoltán Fülöp

  2. Faculty of Computer Science, Technische Universität Dresden, 01062, Dresden, Germany

    Torsten Stüber & Heiko Vogler

Authors
  1. Zoltán Fülöp
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  2. Torsten Stüber
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  3. Heiko Vogler
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Correspondence to Zoltán Fülöp.

Additional information

The work of Z. Fülöp was partially supported by the TÁMOP-4.2.2/08/1/2008-0008 program of the Hungarian National Development Agency.

The work of T. Stüber was partially supported by Deutsche Forschungsgemeinschaft, project DFG VO 1011/4-1.

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Fülöp, Z., Stüber, T. & Vogler, H. A Büchi-Like Theorem for Weighted Tree Automata over Multioperator Monoids. Theory Comput Syst 50, 241–278 (2012). https://doi.org/10.1007/s00224-010-9296-1

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