"Inductive Turing machines" represent the next step in the development of computer science providing better models for contemporary computers and computer networks (Burgin, 2001) and forming an important class of super-recursive algorithms as they satisfy all conditions in the definition of algorithm. Namely, each inductive Turing machine is a type of effective method in which a definite list of well-defined instructions for completing a task, when given an initial state, will proceed through a well-defined series of successive states, eventually terminating in an end-state. The difference between an inductive Turing machine and a Turing machine is that to produce the result a Turing machine has to stop, while in some cases an inductive Turing machine can do this without stopping. Stephen Kleene called procedures that could run forever without stopping by the name "calculation procedure or algorithm" (Kleene 1952:137). Kleene also demanded that such an algorithm must eventually exhibit "some object" (Kleene 1952:137). This condition is satisfied by inductive Turing machines, as their results are exhibited after a finite number of steps, but inductive Turing machines do not always tell at which step the result has been obtained.