# 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 $\epsilon$-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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Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.501-512, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science
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https://hal.inria.fr/inria-00455744
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Soumis le : jeudi 11 février 2010 - 09:56:52
Dernière modification le : jeudi 11 février 2010 - 14:09:43
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• HAL Id : inria-00455744, version 1

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Alexander Kartzow. Collapsible Pushdown Graphs of Level 2 are Tree-Automatic. Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.501-512, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science. 〈inria-00455744〉

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