Superrecursive Features of Interactive Computation

TL;DR

This paper investigates how interactive computation systems can surpass traditional recursive models like Turing machines, identifying five sources of superrecursiveness and conditions for their emergence.

Contribution

It introduces five sources of superrecursiveness in interactive systems and establishes conditions under which these systems can perform non-recursive computations.

Findings

Identified five sources of superrecursiveness in interaction

Proved that excluding these sources limits systems to recursive computations

Provided necessary and sufficient conditions for superrecursiveness

Abstract

Functioning and interaction of distributed devices and concurrent algorithms are analyzed in the context of the theory of algorithms. Our main concern here is how and under what conditions algorithmic interactive devices can be more powerful than the recursive models of computation, such as Turing machines. Realization of such a higher computing power makes these systems superrecursive. We find here five sources for superrecursiveness in interaction. In addition, we prove that when all of these sources are excluded, the algorithmic interactive system in question is able to perform only recursive computations. These results provide computer scientists with necessary and sufficient conditions for achieving superrecursiveness by algorithmic interactive devices.