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On computing the determinant in small parallel time using a small number of processors. (English) Zbl 0541.68019

Summary: The determinant, characteristic polynomial and adjoint over an arbitrary commutative ring with unity can be computed by a circuit with size \(O(n^{3.496})\) and depth O\((log{}^ 2n)\). Furthermore, the circuits can be constructed uniformly (by a log space bounded Turing machine).

MSC:

68Q25 Analysis of algorithms and problem complexity
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