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Structure and importance of logspace-MOD class

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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

.

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Buntrock, G., Damm, C., Hertrampf, U. et al. Structure and importance of logspace-MOD class. Math. Systems Theory 25, 223–237 (1992). https://doi.org/10.1007/BF01374526

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  • DOI: https://doi.org/10.1007/BF01374526

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