Average-Case Computations - Comparing AvgP, HP, and Nearly-P

We examine classes of distributional problems defined in terms of polynomial-time decision algorithms with bounded error probability. The class AvgP [5] has been characterized in [4] using polynomial-time algorithm schemes with benign faults. The class HP [4] extends AvgP by allowing malign faults instead of benign faults. The class AvgHP in turn extends HP by allowing running times to be polynomial on average instead of bounded by a polynomial. Polynomial-time algorithms that decide membership for words of length n with an error probability less than F(n) for some function F lead to the classes F(n)-ErrP [9]. The class Dist-Nearly-P = k 1(1/nk )-ErrP is an instance of the ‘Nearly’-classes as introduced in [11]. We call a distribution µ fair if µ(n) 1/p(n) for some polynomial p(n). We prove:

• Type: Conference
• Year: 2005
• Where: COCO
• Authors: Arfst Nickelsen, Birgit Schelm
• Keywords: Benign Faults, COCO 2005, Polynomial-time Algorithms, Polynomial-time Decision Algorithms