Good lord! Reply after reply after reply that simply refuse to speak to the question you asked!
You're quite right that complexity theory takes us to a hierarchy far richer than simply polynomial and exponentiation [0]. Your question about the emphasis on those two in particular, is a good one. Might be worth submitting on cs.stackexchange.com as a 'soft question'.
You're quite right that complexity theory takes us to a hierarchy far richer than simply polynomial and exponentiation [0]. Your question about the emphasis on those two in particular, is a good one. Might be worth submitting on cs.stackexchange.com as a 'soft question'.
[0] https://en.wikipedia.org/wiki/Time_complexity#Table_of_commo...