Structure and importance of logspace-MOD-classes

Abstract

We refine the techniques of Beigel, Gill, Hertrampf (BGH90) who investigated polynomial time counting classes, in order to make them applicable to the case of logarithmic space. We define the complexity classes MOD_kL and demonstrate their significance by proving that all standard problems of linear algebra over the finite rings Z/kZ are complete for these classes. We then define new complexity classes LogFew and LogFewNL and identify them as adequate logspace versions of Few and FewP. We show that LogFewNL is contained in MODZ_kL and that LogFew is contained in MOD_kL for all k. Also an upper bound for L"L in terms of computation of integer determinants is given from which we conclude that all logspace counting classes are contained in NC"2. (orig.)Available from TIB Hannover: RR 2036(5) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman