On bounds on the number of steps to compute functions

  • Authors:

  • Giorgio Ausiello

  • Affiliations:

  • Istituto per le Applicazioni del Calcolo, Consiglio Nazionale, delle Ricerche -Roma, Italia.

  • Venue:
  • STOC '70 Proceedings of the second annual ACM symposium on Theory of computing
  • Year:
  • 1970

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Abstract

Let f be a partial recursive function defined in terms of other functions g1,...,gn such that f converges if and only if some well defined assertions about the convergency of g1,...,gn hold: then we can find a total function (depending on the number of steps required to compute g1,...,gn) that bounds the step counting function of f almost everywhere f is defined. It is also shown that, in that case, to compute the bound to the step counting function is not much harder than computing the step counting function itself.