Abstract
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.
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Schlicht, P., Stephan, F. (2011). Automata on Ordinals and Linear Orders. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_27
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DOI: https://doi.org/10.1007/978-3-642-21875-0_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21874-3
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