Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

Author Alexander Kartzow

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Alexander Kartzow

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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)


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


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