Abstract
We develop the theory of ω-regular k-partitions (for arbitrary k ≥ 2) that extends the theory around the Wagner hierarchy of regular ω-languages. In particular, we characterize the structure of Wadge degrees of ω-regular k-partitions, prove the decidability of any level of the corresponding hierarchy, establish coincidence of the reducibilities by continuous functions and by functions computed by finite automata on the ω-regular k-partitions.
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Selivanov, V. (2011). A Fine Hierarchy of ω-Regular k-Partitions. 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_28
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DOI: https://doi.org/10.1007/978-3-642-21875-0_28
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