The Non-recursive Power of Erroneous Computation

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

“…The class Dist-Nearly-P extends the notion of Nearly-P to distributional problems. Note that this definition deviates from the distributional version of Nearly-P defined by Schindelhauer and Jakoby in [9].…”

“…Schindelhauer and Jakoby introduced in [9] a scheme for defining error bounded variants of complexity classes. For a given language class C and an error bounding function F they define a class F (n)-Err C of distributional problems by allowing an error probability of F (n) for each input length n. In the following definitions, A∆S stand for the symmetric difference of A and S, i.e.…”

“…In [9], the authors propose to extend the definition of 'Nearly'-classes to distributional problems. This idea leads to the following definition:…”

“…Schindelhauer and Jakoby [9] gave a definition of error bounded classes of distributional problems, F (n)-Err C, where C is a complexity class and F (n) is a bound on the error probability for the words of length n. Similar to the algorithm schemes, the error probability is measured with respect to the input distribution. While Schindelhauer and Jakoby [9] focus on the non-recursive power of the error bounded classes, we investigate the relation of the error bounded classes and HP, in particular of the class Dist-Nearly-P := k 1 1/n k -ErrP.…”

“…While Schindelhauer and Jakoby [9] focus on the non-recursive power of the error bounded classes, we investigate the relation of the error bounded classes and HP, in particular of the class Dist-Nearly-P := k 1 1/n k -ErrP. The class Nearly-P was first introduced by Yamakami in [11,12], but not as a class of distributional problems.…”