Structure and Importance of Logspace-MOD-Classes (1992)
| Citations: | 36 - 1 self |
BibTeX
@MISC{Buntrock92structureand,
author = {Gerhard Buntrock and Carsten Damm and Ulrich Hertrampf and Christoph Meinel},
title = {Structure and Importance of Logspace-MOD-Classes},
year = {1992}
}
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Abstract
. We refine the techniques of Beigel, Gill, Hertrampf [4] who investigated polynomial time counting classes, in order to make them applicable to the case of logarithmic space. We define the complexity classes MOD k L 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 k L and that LogFew is contained in MOD k L 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 . 1 Introduction Valiant [21] defined the class #P of functions f such that there is a nondeterministic polynomial time Turing machine which, on input x, has exactly f(x) accepting computation paths. Many complexity classes in the area betw...
