Abstract für Paper

Random languages for nonuniform complexity classes

Autor: Martin Mundhenk and R. Schuler
Journal of Complexity, 1991
Abstract: A language A is considered to be random for a class C if for every language B in C the fraction of the strings where A and B coincide is approximately 1/2. We show that there exist languages in DSPACE(f(n)) which are random for the non-uniform class DSPACE(g(n))/h(n), where g(n) and h(n) are in o(f(n)), and f(n) is o(n). Non-uniform complexity classes were introduced by Karp and Lipton and allow an advice string that depends only on the length of the input as additional information. This paper extends a result by Wilber who proved bounds for the existence of random languages for (uniform) time and space classes. Huynh provides a result for the special case of ppoly-random languages in EXPSPACE. Here we explore a different method using strings with high generalized Kolmogorov complexity. A characterization of the non-uniform space classes in terms of Kolmogorov complexity is given. This generalizes a result of Balcazar et al where characterizations of the class psppoly are given.

Kontaktadresse: schuler@informatik.uni-ulm.de