Abstract
An infinite and co-infinite setA is bi-immune for a complexity classC if neitherA nor its complement has an infinite subset inC. We prove various equivalent characterizations of this notion. Also, we introduce a stronger version of bi-immunity and show how both notions relate to density and other properties of sets in EXPTIME.
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This research was performed while the authors were visiting the Department of Mathematics, University of California, Santa Barbara, Ca. 93106, U.S.A., and was supported in part by the U.S.A.-Spanish Joint Committee for Educational and Cultural Affairs, by the Deutsche Forschungsgemeinschaft, and by the National Science Foundation under Grants MCS80-11979 and MCS83-12472.
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Balcázar, J.L., Schöning, U. Bi-immune sets for complexity classes. Math. Systems Theory 18, 1–10 (1985). https://doi.org/10.1007/BF01699457
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DOI: https://doi.org/10.1007/BF01699457