Structural Average Case Complexity

Levin introduced an average-case complexity measure, based on a notion of \polynomialon average," and de ned \average-case polynomial-time many-one reducibility" amongrandomized decision problems. We generalize his notions of average-case complexity classes, Random-NP and Average-P. Ben-David et al. use the notation of hC Fi to denote the set of randomized decision problems (L ) such that L is a set in C and is a probability density function in F. This paper introduces AverhC Fi as the class of randomized decision problems (L ) such that L is computed by a type-C machine on -average and is a density function in F. These notations capture allknown average-case complexity classes as, for example, Random-NP = hNP P-compi and Average-P = AverhP i, where P-comp denotes the set of density functions whose distributions are computable in polynomial time, and denotes the set of all density functions. Mainly studied are polynomial-time reductions between randomized decision problems: ...

• Type: Conference
• Year: 1992
• Where: FSTTCS
• Authors: Rainer Schuler, Tomoyuki Yamakami
• Keywords: Average-case Complexity, Average-case Complexity Classes, Decision Problems, FSTTCS 1992, Software Engineering