Abstract
Levin introduced an average-case complexity measure among randomized decision problems. We generalize his notion of Average-P into Aver〈C, F〉, a set of randomized decision problems (L, μ) such that the density function μ is in F and L is computed by a type-C machine in time t (or space t) on μ-average. Mainly studied are two sorts of reductions between randomized problems, average-case many-one and Turing reductions, and structural properties of average-case complexity classes. We give average-case analogs of concepts of classical complexity theory, e.g., the polynomial time hierarchy and self-reducibility.
Supported by the Deutsche Forschungsgemeinschaft, grant No. Scho 302–1.
This work was done while the author was a guest at the University of Ulm in 1991.
The authors would like to thank José Balcázar and Uwe Schöning for organizing workshops in Barcelona and Ulm where many discussions on average-case complexity took place.
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© 1992 Springer-Verlag Berlin Heidelberg
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Schuler, R., Yamakami, T. (1992). Structural average case complexity. In: Shyamasundar, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1992. Lecture Notes in Computer Science, vol 652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56287-7_100
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DOI: https://doi.org/10.1007/3-540-56287-7_100
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