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 logN) algorithm for block sensitivity, an O(N logN) 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.