Algorithms for Boolean Function Query Properties

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We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N².322 log N) algorithm for block sensitivity, an O(N¹.585 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.