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How to Compare the Power of Computational Models

  • Udi Boker
  • Nachum Dershowitz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

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.”

Keywords

Computational Model Turing Machine Multivalued Function Partial Function Recursive Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Udi Boker
    • 1
  • Nachum Dershowitz
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityRamat Aviv, Tel AvivIsrael

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