The complexity of malign ensembles

Abstract

The author analyzes the concept of malignness, which is the property of probability ensembles making the average case running time equal to the worst-case running time for a class of algorithms. He derives lower and upper bounds on the complexity of malign ensembles, which are tight for exponential time algorithms and which show that no polynomial time computable malign ensemble exists for the class of polynomial time algorithms. Furthermore, he shows that for no class of superlinear algorithms does a polynomial time computable malign ensemble exist, unless every language in P has an expected polynomial time constructor.<>