Hypocomputation

Most research into hypercomputation focuses only on machines able to prove stronger results the basic Turing Machine, hence the phrase hypercomputation. However, developing hypercomputational theories requires a deep understanding of computational theories: particularly the boundary between formal and informal theory present in all known computational theories. In this paper we argue for an investigation into computation from the informal side of this boundary, through the investigation of mathematical machines just below the boundary of computation. We will call this class of machines utilising a weaker definition of ‘computation’ hypocomputational machines, and argue that by studying the assumptions used by these machine we should gain insights into the actions of machines such as the Turing Machine lying on the computational boundary. This in turn should provide a much firmer foundation for developing the theories required for hypercomputation, and may help in effort to build ...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: David Love
• Keywords: Computational Theories, CORR 2007, Education, Hypercomputation, Machine