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Variable Tree Automata over Infinite Ranked Alphabets

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Algebraic Informatics (CAI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6742))

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Abstract

We introduce variable tree automata with infinite input ranked alphabets. Our model is based on an underlying bottom-up tree automaton over a finite ranked alphabet containing variable symbols. The underlying tree automaton computes its tree language, and then replaces the variable symbols with symbols from the infinite alphabet following certain rules. We show that the class of recognizable tree languages over infinite ranked alphabets is closed under union and intersection but not under complementation. The emptiness problem is decidable, and the equivalence problem is decidable within special subclasses of variable tree automata. The universality problem is also decidable in a subclass of variable tree automata. We demonstrate the robustness of our model by connecting it to variable finite automata and indicating several characterizations of recognizable tree languages over infinite ranked alphabets.

Research of the first author was supported by the RISC-Linz Transnational Access Programme, project SCIEnce (contract No. 026133) of the European Commission FP6 for Integrated Infrastructures Initiatives.

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Authors and Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Irini-Eleftheria Mens & George Rahonis

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  1. Irini-Eleftheria Mens
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  2. George Rahonis
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Editors and Affiliations

  1. Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Straße 69, 4040, Linz, Austria

    Franz Winkler

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Mens, IE., Rahonis, G. (2011). Variable Tree Automata over Infinite Ranked Alphabets. In: Winkler, F. (eds) Algebraic Informatics. CAI 2011. Lecture Notes in Computer Science, vol 6742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21493-6_16

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  • DOI: https://doi.org/10.1007/978-3-642-21493-6_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21492-9

  • Online ISBN: 978-3-642-21493-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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