Which Bases Admit Non-Trivial Shrinkage of Formulae?

We show that the shrinkage exponent, under random restrictions, of formulae over a nite complete basis B of Boolean functions is strictly greater than 1 if and only if all the functions in B are unate, i.e., monotone increasing or monotone decreasing in each one of their variables. As a consequence, we get non-linear lower bounds on the formula complexity of the parity function over any basis composed only of unate functions