Functions that preserve p-randomness

  • Authors:

  • Stephen A. Fenner

  • Affiliations:

  • -

  • Venue:
  • Information and Computation
  • Year:
  • 2013

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Abstract

We show that polynomial-time randomness (p-randomness) is preserved under a variety of familiar operations, including addition and multiplication by a nonzero polynomial-time computable real number. These results follow from a general theorem: If I@?R is an open interval, f:I-R is a function, and r@?I is p-random, then f(r) is p-random provided1.f is p-computable on the dyadic rational points in I, and 2.f varies sufficiently at r, i.e., there exists a real constant C0 such that either(@?x@?I-{r})[f(x)-f(r)x-r=C] or(@?x@?I-{r})[f(x)-f(r)x-r=