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  • $\begingroup$ Thank you; this seems really promising. I just have no clue where to began to look for such an article. The proof did not seems a trivial corollary to me because, let M be a TM in ASPACE(f,2), let M1 be the part existantial and M2 the universal part. We can not consider anymore M2 to be a coSPACE(f)=SPACVE(f) TM because we should take the input of M1 in the input tape. But yes, there is certainly something to do using directly their proof. Even if I did not though off using a number "a(n)" of alternation. Thank you again $\endgroup$ Commented Aug 25, 2010 at 4:39