Nonuniform complexity and the randomness of certain complete languages

Abstract

This paper contains further study of the randomness properties of languages. The connection between time-/space-bounded Kolmogorov complexity and nonuniform complexity defined by grammar and automaton size is investigated. We show that certain languages that are complete under nonuniform one-way log-space reductions are weakly random with respect to other language classes contained in P. For example, it is shown that every context-free language that is complete under nonuniform one-way log-space reductions is weakly random with respect to the class of deterministic context-free languages, and every deterministic context-free language that is complete under nonuniform one-way log-space reductions is weakly random with respect to the class of linear context-free languages.