We argue that there is currently no satisfactory general framework for comparing the extensional computational power of arbitrary computational models operating over arbitrary domains. We propose a conceptual framework for comparison, by linking computational models to hypothetical physical devices. Accordingly, we deduce a mathematical notion of relative computational power, allowing the comparison of arbitrary models over arbitrary domains. In addition, we claim that the method commonly used in the literature for "strictly more powerful" is problematic, as it allows for a model to be more powerful than itself. On the positive side, we prove that Turing machines and the recursive functions are "complete" models, in the sense that they are not susceptible to this anomaly, justifying the standard means of showing that a model is "hypercomputational."
|Number of pages||11|
|Journal||Lecture Notes in Computer Science|
|State||Published - 2005|
|Event||First Conference on Computability in Europe, CiE 2005: New Computational Paradigms - Amsterdam, Netherlands|
Duration: 8 Jun 2005 → 12 Jun 2005