Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

Details Collapsible Pushdown Graphs of Level 2 are Tree-Automatic Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

2009-12-21

arxiv.org/abs/0912.4110v2

Mathematics

Logic

12 pages Accepted for STACS 2010

Scientific paper

We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even when we allow $\epsilon$-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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