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Nov 29, 2010 at 1:24 comment added Tsuyoshi Ito @Hsien-Chih Chang: Fenner, Fortnow, Kurtz and Li 2003 define a notion called “relativizable complexity class,” which is a mapping C which takes a language A to a complexity class C^A satisfying certain properties. This notion may be useful to make the original question (revision 1 or the question) rigorous without restricting the class C to a specific class.
Nov 28, 2010 at 16:18 comment added Hsien-Chih Chang 張顯之 You are correct; I did not aware that $\mathsf{C^O}$ may be not well-defined. I'll try to modify my question, please correct me if it is still problematic.
Nov 28, 2010 at 2:12 history answered John Watrous CC BY-SA 2.5