On Lower Bounds for Multiplicative Circuits and Linear Circuits in Noncommutative Domains
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In this paper we show some lower bounds for the size of multiplicative circuits computing multi-output functions in some noncommutative domains such as monoids and finite groups. We also introduce and study a generalization of linear circuits in which the goal is to compute MY where Y is a vector of indeterminates and M is a matrix whose entries come from noncommutative rings. We show some lower bounds in this setting as well.
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- 8.Nisan, N.: Lower bounds for non-commutative computation (extended abstract). In: STOC, pp. 410–418 (1991)Google Scholar