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 Presentations of Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Collapsible Pushdown Automata and Recursion Schemes
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Adding nesting structure to words
Journal of the ACM (JACM)
Linear orders in the pushdown hierarchy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Regular Languages of Nested Words: Fixed Points, Automata, and Synchronization
Theory of Computing Systems
Unsafe grammars and panic automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Regular sets of higher-order pushdown stacks
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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We introduce two natural variants of prefix rewriting on nested-words. One captures precisely the transition graphs of order-2 pushdown automata and the other precisely those of order-2 collapsible pushdown automata (2-CPDA). To our knowledge this is the first precise ‘external' characterisation of 2-CPDA graphs and demonstrates that the class is robust and hence interesting in its own right. The comparison with our characterisation for 2-PDA graphs also gives an idea of what ‘collapse means' in terms outside of higher-order automata theory. Additionally, a related construction gives us a decidability result for first-order logic on a natural subclass of 3-CPDA graphs, which in some sense is optimal.