Algorithms for Boolean Function Query Properties

We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for tree decomposition,' and an O(N) algorithm for quasisymmetry.’ These algorithms are based on new insights into the structure of Boolean functions that may be of independent interest. We also give a subexponential-time algorithm for the space-bounded quantum query complexity of a Boolean function. To prove this algorithm correct, we develop a theory of limited-precision representation of unitary operators, building on work of Bernstein and Vazirani.