What Percentage of Programs Halt?

  • Laurent Bienvenu
  • Damien Desfontaines
  • Alexander Shen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9134)

Abstract

Fix an optimal Turing machine U and for each n consider the ratio \(\rho ^U_n\) of the number of halting programs of length at most n by the total number of such programs. Does this quantity have a limit value? In this paper, we show that it is not the case, and further characterise the reals which can be the limsup of such a sequence \(\rho ^U_n\). We also study, for a given optimal machine U, how hard it is to approximate the domain of U from the point of view of coarse and generic computability.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Laurent Bienvenu
    • 1
  • Damien Desfontaines
    • 2
  • Alexander Shen
    • 3
    • 4
  1. 1.LIAFA - CNRS and Université Paris 7ParisFrance
  2. 2.Google Inc.ZurichSwitzerland
  3. 3.LIRMM - CNRS and Université MontpellierMontpellierFrance
  4. 4.On leave from IITP RASMoscowRussia

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