Circuit complexity of testing square-free numbers

Authors:
Anna Bernasconi;Igor Shparlinski
Affiliations:
Institut für Informatik, Technische Universität München, München, Germany;School of MPCE, Macquarie University, Sydney, Australia
Venue:
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Year:
1999

Citing 11
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Abstract

In this paper we extend the area of applications of the Abstract Harmonic Analysis to the field of Boolean function complexity. In particular, we extend the class of functions to which a spectral technique developed in a series of works of the first author can be applied. This extension allows us to prove that testing square-free numbers by unbounded fan-in circuits of bounded depth requires a superpolynomial size. This implies the same estimate for the integer factorization problem.