• Publications
  • Influence
Strictness of the Collapsible Pushdown Hierarchy
TLDR
This paper gives the first known examples that separate the levels of the collapsible pushdown graph hierarchy and the hierarchy of trees generated by higher-order recursion schemes, confirming the open conjecture that higher orders allow one to generate more graphs and more trees. Expand
Collapsible Pushdown Graphs of Level 2 are Tree-Automatic
TLDR
It is shown that graphs generated by collapsible pushdown systems of level $2$ are tree-automatic, and their \FO theories are decidable, even when expanded by a reachability predicate. Expand
Satisfiability of ECTL⁎ with constraints
TLDR
It is shown that satisfiability and finite satisfiability for ECTL * with equality-, order-, and modulo-constraints over Z are decidable, and this greatly improves the previously known decidability results for certain fragments of CTL *, e.g., the existential and positive fragments and EF. Expand
A Pumping Lemma for Collapsible Pushdown Graphs of Level 2
TLDR
This pumping lemma even applies to epsilon-contractions of level 2 collapsible pushdown graphs and improves the bounds of Hayashi's Pumping lemma for indexed languages. Expand
Collapsible Pushdown Graphs of Level 2 are Tree-Automatic
  • Alexander Kartzow
  • Computer Science, Mathematics
  • Log. Methods Comput. Sci.
  • 21 December 2009
TLDR
It is shown that graphs generated by collapsible pushdown systems of level 2 are tree-automatic, even if epsilon-contractions and reachability predicates for pairs of configurations are allowed, whence their first-order logic theories are decidable. Expand
Satisfiability of CTL* with Constraints
We show that satisfiability for CTL* with equality-, order-, and modulo-constraints over ℤ is decidable. Previously, decidability was only known for certain fragments of CTL*, e.g., the existentialExpand
Satisfiability of ECTL* with Tree Constraints
TLDR
This work shows that satisfiability of EHD with constraints is decidable over semi-linear orders, and introduces Ehrenfeucht-Fraisse-games for Weak MSO+B and uses them to show that the infinite (order) tree does not have property EHD. Expand
First-Order Model Checking on Generalisations of Pushdown Graphs
TLDR
It is proved that first-order logic extended by Ramsey quantifiers is decidable on all tree-automatic structures. Expand
Structures without Scattered-Automatic Presentation
TLDR
This paper proves the following limitations on the class of \(\mathfrak{L}\)-automatic structures for a fixed \(\ mathfrak {L}\) of finite condensation rank 1 + α. Expand
Tree-Automatic Well-Founded Trees
TLDR
It is shown that the isomorphism problem for tree-automatic well-founded trees is complete for level $\Delta^0_{\omega^ \omega}$ of the hyperarithmetical hierarchy (under Turing-reductions). Expand
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