Structure and importance of logspace-MOD class

Abstract

We refine the techniques of Beigelet al. [4] who investigated polynomial-time counting classes, in order to make them applicable to the case of logarithmic space. We define the complexity classes and demonstrate their significance by proving that all standard problems of linear algebra over the finite ringsZ/kZ are complete for these classes. We then define new complexity classes LogFew and LogFew and identify them as adequate logspace versions of Few and Few . We show that LogFew is contained in and that LogFew is contained in for allk. Also an upper bound for in terms of computation of integer determinants is given from which we conclude that all logspace counting classes are contained in .