An automata-theoretical characterization of the OI-hierarchy
Information and Control
Pushdown machines for the macro tree transducer
Theoretical Computer Science
Handbook of formal languages, vol. 1
Indexed Grammars—An Extension of Context-Free Grammars
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A short solution of the HDT0L sequence equivalence problem
Theoretical Computer Science
On Infinite Terms Having a Decidable Monadic Theory
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
ICAL '99 Proceedings of the 26th 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
Iterated pushdown automata and complexity classes
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Grammars with macro-like productions
SWAT '68 Proceedings of the 9th Annual Symposium on Switching and Automata Theory (swat 1968)
Theory of Computing Systems
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Sequences of numbers (either natural integers, or integers or rational) of level k ∈ IN have been defined in [FS06] as the sequences which can be computed by deterministic pushdown automata of level k. We extend this definition to sequences of words indexed by words. We give characterisations of these sequences in terms of "higher-order" L-systems. In particular sequences of rational numbers of level 3 are characterised by polynomial recurrences (which generalize the Precurrent sequences studied in [Sta80]). The equality problem for sequences of rational numbers of level 3 is shown decidable.