More than two decades elapsed since Levin set forth a theory of average-case complexity. In this survey we present the basic aspects of this theory as well as some of the main results regarding it. The current presentation deviates from our old “Notes on Levin’s Theory of Average-Case Complexity” (ECCC, TR97-058, 1997) in several aspects.

X k=1 z 0k A0;k(z M)Mi01(z M): (41) This formula makes transparent exactly what happens in a recursive computation of the correlation functions. At every stage i, we have the Z-transform at points M 0i n of the appropriate function. In going to the (i + 1)st stage, the rst term Mi01(z M) ensures that values at the previous stage are retained at the even points, while the second term interpolate...

Based on the increasing property of ratio of average reversed hazard rates of two non-negative random variables a new stochastic order for the sake of comparison of two lifetime distributions is proposed. This stochastic order admits some distinguishing properties. In order to illustrate the obtained results, a semi-parametric model which is called reverse hazard power and a mixture model of pr...

uses of ‘average’ differ in several ways from concrete uses. In sentences of the sort we are focusing on, in which ‘average’ is part of a definite description in subject position, the truth conditions of examples with concrete ‘average’ can typically be paraphrased as generic statements. For example, (4a) is true just in case it generally holds that individuals who are New Yorkers and are avera...

When approached by a potential predator, individuals must decide when to flee. Individuals could assess risk by monitoring their distance from an approaching threat or by monitoring the expected time that the predator would take to reach them. Theory predicts, and empirical studies support the hypothesis, that some species maymaintain a temporal margin of safety and therefore monitor the expect...