On the average sensitivity of testing square-free numbers

Authors:
Anna Bernasconi;Carsten Damm;Igor E. Shparlinski
Affiliations:
Institut für Informatik, Technische Universität München, München, Germany;Fachbereich für Informatik, Universität Trier, Trier, Germany;School of MPCE, Macquarie University, Sydney, NSW, Australia
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain a linear lower bound on the average sensitivity of the Boolean function deciding whether a given integer is square-free. This result allows us to derive a quadratic lower bound for the formula size complexity of testing square-free numbers and a linear lower bound on the average decision tree depth. We also obtain lower bounds on the degrees of exact and approximative polynomial representations of this function.