How to Compare the Power of Computational Models

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How to Compare the Power of Computational Models
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.”
Udi Boker, Nachum Dershowitz
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where CIE
Authors Udi Boker, Nachum Dershowitz
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