Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

Kartzow, Alexander

doi:10.4230/LIPIcs.STACS.2010.2480

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Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

Author Alexander Kartzow

Part of: Volume: 27th International Symposium on Theoretical Aspects of Computer Science (STACS 2010)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NoDerivs 3.0 Unported license
Publication Date: 2010-03-09

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DOI: 10.4230/LIPIcs.STACS.2010.2480
URN: urn:nbn:de:0030-drops-24801

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Keywords

Tree-automatic structures
collapsible pushdown graphs
collapsible pushdown systems
first-order decidability
reachability

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Abstract

We show that graphs generated by collapsible pushdown systems of level $2$ are tree-automatic. Even when we allow $\varepsilon$-contractions and add a reachability predicate (with regular constraints) for pairs of configurations, the structures remain tree-automatic. Hence, their \FO theories are decidable, even when expanded by a reachability predicate. As a corollary, we obtain the tree-automaticity of the second level of the Caucal-hierarchy.

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Alexander Kartzow. Collapsible Pushdown Graphs of Level 2 are Tree-Automatic. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 501-512, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010) https://doi.org/10.4230/LIPIcs.STACS.2010.2480

Author Details

Alexander Kartzow

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