Abstract

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 time complexity classes E and E2 . Moreover, we treat time-bounded genericity and stochasticity concepts which are weaker than time-bounded randomness but which suffice for many of the applications in complexity theory. 1 Introduction The first attempt for defining the concept of a random sequence goes back to von Mises [vM19] in 1919. He proposed that an infinite 0-1-sequence S should be considered to be random if, in the limit, the number of the occurrences of the 0s and 1s in S is the same (i.e. the sequence S satisfies the law of large numbers) and if this stability property is inherited by every infinite subsequence of S obtained by an admissible selection rule. A fuzzyness in this concept, due to the lack of a formal definition of admissibility was later eliminated by Church [Ch40] in 1940, who proposed t...

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