 Besides these variants on the Turing machine model, there are also variants that result in models which capture, in some well-defined sense, more than the (Turing)-computable functions. Examples of such models are oracle machines (Turing 1939), infinite-time Turing machines (Hamkins &amp; Lewis 2008) and accelerating Turing machines (Copeland 2002). There are various reasons for introducing such stronger models. Some are well-known models of computability or recursion theory and are used in the theory of higher-order recursion and relative computability (oracle machines); others, like the accelerating machines, were introduced in the context of  supertasks  and the idea of providing physical models that “compute” functions which are not Turing-computable.