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Projection for Büchi Tree Automata with Constraints Between Siblings

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Developments in Language Theory (DLT 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11088))

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Abstract

We consider an extension of tree automata on infinite trees that can check equality and disequality constraints between direct subtrees of a node. Recently, it has been shown that the emptiness problem for these kind of automata with a parity acceptance condition is decidable and that the corresponding class of languages is closed under Boolean operations. In this paper, we show that the class of languages recognizable by such tree automata with a Büchi acceptance condition is closed under projection. This construction yields a new algorithm for the emptiness problem, implies that a regular tree is accepted if the language is non-empty (for the Büchi condition), and can be used to obtain a decision procedure for an extension of monadic second-order logic with predicates for subtree comparisons.

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Notes

  1. 1.

    A parity condition assigns priorities (natural numbers) to states and is satisfied in a state sequence if the maximal priority that appears infinitely often is even. A Büchi condition corresponds to a parity condition with priorities 1 and 2.

  2. 2.

    The use of cylindrification is often not mentioned explicitly in translations from logic to automata because for standard automata it is a trivial operation.

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Authors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Patrick Landwehr & Christof Löding

Authors
  1. Patrick Landwehr
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  2. Christof Löding
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Correspondence to Patrick Landwehr .

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Editors and Affiliations

  1. National Archives of Japan, Tokyo, Japan

    Mizuho Hoshi

  2. The University of Electro-Communications, Tokyo, Japan

    Shinnosuke Seki

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Landwehr, P., Löding, C. (2018). Projection for Büchi Tree Automata with Constraints Between Siblings. In: Hoshi, M., Seki, S. (eds) Developments in Language Theory. DLT 2018. Lecture Notes in Computer Science(), vol 11088. Springer, Cham. https://doi.org/10.1007/978-3-319-98654-8_39

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  • DOI: https://doi.org/10.1007/978-3-319-98654-8_39

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-98654-8

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