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URN: urn:nbn:de:0030-drops-24801
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### Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

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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.

### BibTeX - Entry

@InProceedings{kartzow:LIPIcs:2010:2480,
author =	{Alexander Kartzow},
title =	{{Collapsible Pushdown Graphs of Level 2 are Tree-Automatic}},
booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
pages =	{501--512},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-16-3},
ISSN =	{1868-8969},
year =	{2010},
volume =	{5},
editor =	{Jean-Yves Marion and Thomas Schwentick},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},