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Application of separability and independence notions for proving lower bounds of circuit complexity

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Abstract

This note consists of two independent parts. In the first part the concept of an (m,c)-system for a set of linear forms is introduced, and a lower bound is obtained for the algebraic complexity of the computation of (m,c)-systems on algebraic circuits of a special form. In the second part, the notion of an ℓ-independent set of boolean functions is introduced and a lower bound is obtained for a certain complexity measure for circuits of boolean functions computing ℓ-independent sets. As a corollary it is shown that the standard algorithm for multiplying matrices or polynomials may be realized by a circuit of boolean functions in a way that is optimal with respect to a selected complexity measure.

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Literature cited

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Authors
  1. D. Yu. Grigor'ev
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Additional information

Translated from Zapiski Nauchykh Seminarov Leningradskogo Otdeleniya Mathematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 60, pp. 38–48, 1976. Main results presented December 12, 1974 and May 29, 1975.

The author would like to express his deep appreciation to A. O. Slisenko for his help.

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Grigor'ev, D.Y. Application of separability and independence notions for proving lower bounds of circuit complexity. J Math Sci 14, 1450–1457 (1980). https://doi.org/10.1007/BF01693976

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  • DOI: https://doi.org/10.1007/BF01693976

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