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    A note on time hierarchies for reasonable semantic classes without advice

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    We show time hierarchies for reasonable semantic classes without advice by eliminating the constant bits of advice in previous results.The elimination is done by a contrapositive argument that for any reasonable computational model,let CTIME(f(n))/g(n)\text{CTIME}(f(n))/{g(n)} denote the set of all languages decide by machines running in time O(f(n))O(f(n)) with advice of g(n)g(n) bits in that model, if CTIME(t(n))βŠ†CTIME(T(n))/A(n)\text{CTIME}(t(n))\subseteq \text{CTIME}(T(n))/{A(n)} then CTIME(t(n))/aβŠ†CTIME(T(n))/a+2aA(n)\text{CTIME}(t(n))/a \subseteq \text{CTIME}(T(n))/{a+2^aA(n)} where aa is a constant integer.Comment: There is a mistake in the argument,take BPTIME as example, after fixing the advice,the new uniform probablistic machine probably won't satisfy BP promise any more. Pointed out by Professor Fortno
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