Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

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.Comment: 12 pages Accepted for STACS 201

Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even if we allow epsilon-contractions and reachability predicates (with regular constraints) for pairs of configurations, the structures remain tree-automatic whence their first-order logic theories are decidable. As a corollary we obtain the tree-automaticity of the second level of the Caucal-hierarchy.Comment: Journal version of arXiv:0912.4110, accepted for publication in LMC

First-Order Model Checking on Generalisations of Pushdown Graphs

We study the first-order model checking problem on two generalisations of pushdown graphs. The first class is the class of nested pushdown trees. The other is the class of collapsible pushdown graphs. Our main results are the following. First-order logic with reachability is uniformly decidable on nested pushdown trees. Considering first-order logic without reachability, we prove decidability in doubly exponential alternating time with linearly many alternations. First-order logic with regular reachability predicates is uniformly decidable on level 2 collapsible pushdown graphs. Moreover, nested pushdown trees are first-order interpretable in collapsible pushdown graphs of level 2. This interpretation can be extended to an interpretation of the class of higher-order nested pushdown trees in the collapsible pushdown graph hierarchy. We prove that the second level of this new hierarchy of nested trees has decidable first-order model checking. Our decidability result for collapsible pushdown graph relies on the fact that level 2 collapsible pushdown graphs are uniform tree-automatic. Our last result concerns tree-automatic structures in general. We prove that first-order logic extended by Ramsey quantifiers is decidable on all tree-automatic structures.Comment: phd thesis, 255 page

Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

We show that graphs generated by collapsible pushdown systems of level 2 aretree-automatic. Even if we allow epsilon-contractions and reachabilitypredicates (with regular constraints) for pairs of configurations, thestructures remain tree-automatic whence their first-order logic theories aredecidable. As a corollary we obtain the tree-automaticity of the second levelof the Caucal-hierarchy.Comment: Journal version of arXiv:0912.4110, accepted for publication in LMC

A pumping lemma for collapsible pushdown graphs of level 2

We present a pumping lemma for the class of collapsible pushdown graphs of level 2. This pumping lemma even applies to the ε-contractions of level 2 collapsible pushdown graphs. Our pumping lemma also improves the bounds of Hayashi’s pumping lemma for indexed languages

Collapsible Pushdown Graphs of Level 2 are Tree-Automatic

International audienceWe 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