The first edition of the monograph Information and Randomness: An Algorithmic Perspective
by Crist ian Calude was published in 1994. In my Foreword I said:" The research in …

Recent results on the internal, measure-theoretic structure of the exponential time
complexity classes E= DTIME (2/sup linear/) and E/sub 2/= DTIME (2/sup polynomial/) are …

We survey recent results on resource-bounded measure and randomness in structural
complexity theory. In particular, we discuss applications of these concepts to the exponential …

Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more
than a negligible subset of exponential time), it is shown that there is a language that is⩽ TP …

We present a notion of resource-bounded measure for P and other subexponential-time
classes. This generalization is based on Lutz's notion of measure, but overcomes the …

We introduce and study resource bounded random sets based on Lutz's concept of resource
bounded measure [7, 8]. We concentrate on nc-randomness (c⩾ 2) which corresponds to the …

We introduce balanced t (n)-genericity which is a refinement of the genericity concept of
Ambos-Spies, Fleischhack and Huwig [2] and which in addition controls the frequency with …

Measure-theoretic aspects of the ≦_m^P-reducibility structure of the exponential time
complexity classes E=DTIME(2^linear) and E_2=DTIME(2^polynomial) are investigated …

Recently, Lutz [14, 15] introduced a polynomial time bounded version of Lebesgue measure.
He and others (see eg [11, 13–18, 20]) used this concept to investigate the quantitative …

We prove that if strong pseudorandom number generators exist, then the class of languages
that have polynomial-sized circuits (P/poly) is not measurable within exponential time, in …