Super-recursive Algorithms and Modes of Computation

Abstract

According to the contemporary computer science, working in the functional recursive mode, computers and computer networks function as recursive algorithms. At the same time, working in the functional super-recursive mode, such as inductive or limit modes, computers and computer networks function as super-recursive algorithms (Burgin, 2005). While one group of notable researchers claims that interactive computation is more powerful than Turing machines (cf., for example, (Wegner, 1997)), others argue that the Church-Turing Thesis, which equates algorithms with Turing machines, still holds and that interaction does not add anything new (cf., for example, (Prasse and Rittgen, 1998) and (Van Leeuwen and Wiedermann, 2000). The cause of this misunderstanding is that the standard computability theory does not take into account time and space where real computers and networks function. Under such artificial conditions, interacting abstract automata and algorithms cannot achieve super-recursive power if they are all recursive as it is proved in (Burgin, 2006). In contrast to this, even a finite system of interacting recursive automata or algorithms functioning in the real time and space can become super-recursive (Burgin, 2007).In this paper, we study modes of information processing in abstract automata, material, e.g., physical or biological, computers and networks. Computational and networking practice shows that taking into account modes of information processing is important for efficient design of distributed hardware and software systems. Modes of computation studied here for abstract automata are actually directions and explanations of how to utilize computers and network computations.