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Sorry for my english. I don't know if I use the right terminology. DEF.: F is a compile-time function if exist the Turing machine which run-time doesn't depend on the input. I know that for the demostration I need to build a Turing-machine but I don't know how to procede; another metod I though is considering 2^F(x) a composition of compile-time function, because is compotition of 2 applied F(x) times and the text of the exercise garantees that F(x) is compile-time. For the last method I don't know if constant are compile-time.

I tried appling speed-up time but it wasn't useful. This is a exercise proposed by my professor during the course of "calcolability and complessity" (literal translation); I'm having a lot of difficulty with finding exercise and explanation online (the language doesn't help) so if anyone suggest some exercises, texts or web-sites I would be really grateful.

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