We investigate structures recognizable by α-automata with running time a limit ordinal α. The domain of such a structure consists of finite α-words with gaps. An α-automaton resembles a finite automaton but has a limit rule which maps the set of states which appear cofinally often before the limit to a limit state. We determine the suprema of the α-automatic ordinals and the ranks of α-automatic linear orders. The power of α-automata increases with every power of ω. © 2011 Springer-Verlag.
CITATION STYLE
Schlicht, P., & Stephan, F. (2011). Automata on ordinals and linear orders. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6735 LNCS, pp. 252–259). https://doi.org/10.1007/978-3-642-21875-0_27
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