Foundational analyses of computation

  • Authors:
  • Yuri Gurevich

  • Affiliations:
  • Microsoft Research, One Microsoft Way, Redmond, WA, United States of America

  • Venue:
  • CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
  • Year:
  • 2012

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Abstract

How can one possibly analyze computation in general? The task seems daunting if not impossible. There are too many different kinds of computation, and the notion of general computation seems too amorphous. As in quicksand, one needs a rescue point, a fulcrum. In computation analysis, a fulcrum is a particular viewpoint on computation that clarifies and simplifies things to the point that analysis becomes possible. We review from that point of view the few foundational analyses of general computation in the literature: Turing's analysis of human computations, Gandy's analysis of mechanical computations, Kolmogorov's analysis of bit-level computation, and our own analysis of computation on the arbitrary abstraction level.