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We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G ∼ = H. For several decades, the n log p n+O(1) generator-enumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first(More)
We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the n log p n+O(1) generator-enumeration algorithm. In previous work with Fabian Wagner, we showed an n (1/2) log p n+O(log n/ log log n) time algorithm for testing isomorphism of p-groups by(More)
We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation which is selected according to internal random coins. We show new exponential quantum speedups which may be obtained over classical algorithms in this oracle model. Even stronger, we describe several problems which are impossible to solve(More)
BACKGROUND AND OBJECTIVES Continuity of care is one of the presumed advantages of longitudinal residencies. However, it is not clear how well such residencies provide continuity of care, and, further, there is no recognized acceptable rate of good continuity. We compared traditional and longitudinal residencies to determine the extent to which the residents(More)
Extended Superposed Quantum State Initialization Using Disjoint Prime Im-plicants (ESQUID) is a new algorithm for generating quantum arrays for the purpose of initializing a desired quantum superposition. The quantum arrays generated by this algorithm almost always use fewer gates than other algorithms and in the worst case use the same number of gates.(More)