On the Theory of Average Case Complexity

This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works Levin 84, Gurevich 87, Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. Our results include: the equivalence of search and decision problems in the context of average case complexity an initial analysis of the structure of distributional-NP (i.e. NP problems coupled with \simple distributions") under reductions which preserve average polynomial-time a proofthat ifallof distributional-NP is in average polynomial-timethen non-deterministic exponential-time equals deterministic exponential time (i.e., a collapse in the worst case hierarchy) de nitionsand basic theoremsregarding other complexityclasses such as average log-space. An exposition of the basic de nitions suggested by Levin and suggestions for some alternative de nitions are provided as well. Remark...

• Type: Conference
• Year: 1989
• Where: STOC
• Authors: Shai Ben-David, Benny Chor, Oded Goldreich, Michael Luby
• Keywords: Algorithms, Average Case Complexity, Average Polynomial-time, Polynomial-timethen Non-deterministic Exponential-time, STOC 1989