On super-turing computing power and hierarchies of artificial general intelligence systems

Abstract

Using the contemporary view of computing exemplified by recent models and results from non-uniform complexity theory we investigate the computational power of artificial general intelligence systems (AGISs). We show that in accordance with the so-called Extended Turing Machine Paradigm such systems can be seen as non-uniform evolving interactive systems whose computational power surpasses that of classical Turing machines. Our results shed light to the question asked by R. Penrose concerning the mathematical capabilities of human mathematicians which seem to go beyond classical computability. We also show that there is an infinite hierarchy of AGISs each of which is capable to solve strictly more problems than its predecessors in the hierarchy.