Hypercomputational Models

Abstract

Hypercomputers are physical or conceptual machines capable of performing non-recursive tasks; their behavior lies beyond the so-called “Turing limit.” Recent decades have seen many hypercomputational models in the literature, but in many cases we know neither how these models are related to one another, nor the precise reasons why they are so much more powerful than Turing machines. In this chapter we start by considering Turing’s machine-based model of computation, and identify various structural constraints. By loosening each of these constraints in turn, we identify various classes of hypercomputational device, thereby generating a basic taxonomy for hypercomputation itself.