Iterated stack automata and complexity classes
Information and Computation
Monadic second-order definable graph transductions: a survey
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
On Infinite Terms Having a Decidable Monadic Theory
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
On Infinite Transition Graphs Having a Decidable Monadic Theory
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Higher-Order Pushdown Trees Are Easy
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Automatic linear orders and trees
ACM Transactions on Computational Logic (TOCL)
On the structure of graphs in the Caucal hierarchy
Theoretical Computer Science
Regular and algebraic words and ordinals
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Fundamenta Informaticae
Regular sets of higher-order pushdown stacks
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Hierarchies of infinite structures generated by pushdown automata and recursion schemes
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
An undecidable property of context-free linear orders
Information Processing Letters
Scattered context-free linear orderings
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Regular sets over extended tree structures
Theoretical Computer Science
Hausdorff rank of scattered context-free linear orders
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Prefix rewriting for nested-words and collapsible pushdown automata
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
A context-free linear ordering with an undecidable first-order theory
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
The FC-rank of a context-free language
Information Processing Letters
Theory of Computing Systems
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We investigate the linear orders belonging to the pushdown hierarchy. Our results are based on the characterization of the pushdown hierarchy by graph transformations due to Caucal and do not make any use of higher-order pushdown automata machinery. Our main results show that ordinals belonging to the n-th level are exactly those strictly smaller than the tower of ω of height n + 1. More generally the Hausdorff rank of scattered linear orders on the n-th level is strictly smaller than the tower of ω of height n. As a corollary the Cantor-Bendixson rank of the tree solutions of safe recursion schemes of order n is smaller than the tower of ω of height n. As a spin-off result, we show that the ω-words belonging to the second level of the pushdown hierarchy are exactly the morphic words.