The average sensitivity of square-freeness
- Cite this article as:
- Bernasconi, A., Damm, C. & Shparlinski, I. Comput. complex. (2000) 9: 39. doi:10.1007/PL00001600
We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain an asymptotic formula, having a linear main term, for 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 approximate polynomial representations of this function.