An explicit recursion-theoretic definition of a random sequence or random set of natural numbers was given by Martin-Löf in 1966. Other approaches leading to the notions of n-randomness and weak… (More)

It is well known that the discrete Sierpinski triangle can be defined as the nonzero residues modulo 2 of Pascal’s triangle, and that from this definition one can easily construct a tileset with… (More)

Most research on resource-bounded measure and randomness has focused on the uniform probability density, or Lebesgue measure, on {0, 1}∞; the study of resource-bounded measure theory with respect to… (More)

General purpose object-oriented programs typically aren't embarrassingly parallel. For these applications, finding enough concurrency remains a challenge in program design. To address this challenge,… (More)

Resource-bounded measure as originated by Lutz is an extension of classical measure theory which provides a probabilistic means of describing the relative sizes of complexity classes. Lutz has… (More)

Any plausible characterization of what it means for an infinite sequence to be random is likely to incorporate the common notion that one random sequence should not contain any information about any… (More)

Discrete self-similar fractals have been used as test cases for self-assembly, both in the laboratory and in mathematical models, ever since Winfree exhibited a tile assembly system in which the… (More)

Results on random oracles typically involve showing that a class {X : P (X)} has Lebesgue measure one, i.e., that some property P (X) holds for “almost every X.” A potentially more informative… (More)

A bounded Kolmogorov-Loveland selection rule is an adaptive strategy for recursively selecting a subsequence of an infinite binary sequence; such a subsequence may be interpreted as the query… (More)