Abstract
We study the complexity of some computational problems on finite black-box rings whose elements are encoded as strings of a given length and the ring operations are performed by a black-box oracle. We give a polynomial-time quantum algorithm to compute a basis representation for a given black-box ring. Using this result we obtain polynomial-time quantum algorithms for several natural computational problems over black-box rings.
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Arvind, V., Das, B., Mukhopadhyay, P. (2006). The Complexity of Black-Box Ring Problems. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_15
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DOI: https://doi.org/10.1007/11809678_15
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