For a wide class of  models, a significant discovery was that efficient simulations can be found. For instance, it might at first appear that the model \(\mathfrak{A}\) allows for considerably more efficient implementations of familiar algorithms than does the model \(\mathfrak{T}\) in virtue of the fact that a RAM machine can access any of its registers in a single step whereas a Turing machine may move its head only a single cell at a time. Nonetheless it can be shown that there exists a simulation of the RAM model by the Turing machine model with cubic time overhead and constant space overhead – i.e. \(o_t(t(n)) \in O(t(n)^3)\) and \(o_s(s(n)) \in O(s(n))\) (Slot and Emde Boas 1988). On the basis of this and related results, Emde Boas (1990) formulated the following proposal to characterize the relationship between reference models which might be used for defining time and space complexity: