Abstract
We design an algorithm for computing the generalized (algebraic circuits with root extracting; cf. Pippenger [J. Comput. System Sci., 22 (1981), pp. 454--470], Ja'Ja' [Proc. 22nd IEEE FOCS, 1981, pp. 95--100], Grigoriev, Singer, and Yao [ SIAM J. Comput., 24 (1995), pp. 242--246]) additive complexity of any rational function. It is the first computability result of this sort on the additive complexity of algebraic circuits.
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