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Abstract: In this paper we describe a new technique for obtaining lower bounds on restriced classes of nonmonotone arithmetic circuits. The heart of this technique is a complexity measure for multivariate polynomials, based on the linear span of their partial derivatives. We use the technique to obtain new lower bounds for computing symmetric polynomials and iterated matrix products. 1 Introduction Despite much effort there are still essentially no lower bounds known for general models of computation... (Update)
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BibTeX entry: (Update)
N. Nisan, A.W. Widgerson, "Lower bounds on arithmetic circuits via partial derivatives," 36 th Ann. IEEE Symp. Foundations of CS, pp. 16-25, 1995. http://citeseer.ist.psu.edu/nisan95lower.html More
@inproceedings{ nisan95lower,
author = "Nisan and Wigderson",
title = "Lower Bounds on Arithmetic Circuits via Partial Derivatives (Preliminary Version)",
booktitle = "{FOCS}: {IEEE} Symposium on Foundations of Computer Science ({FOCS})",
year = "1995",
url = "citeseer.ist.psu.edu/nisan95lower.html" }
Citations (may not include all citations):44 Vermeidung von divisionen (context) - Strassen - 1973
42 Fast parallel computation of polynomials using few processor.. (context) - Valiant, Skyum et al. - 1983
22 Lower Bounds for Non-Commutative Computation (context) - Nisan - 1991
16 Algebraic complexity theory (context) - Gathen - 1988
10 Negation can be exponentially powerful (context) - Valiant - 1979
7 On interpolation by analytic functions with special properti.. (context) - Smolensky - 1990
6 the depth complexity of formulas (context) - Shamir, Snir - 1980
4 A Direct Version of Shamir and Snir's Lower Bounds on Monoto.. (context) - Tiwari, Tompa - 1994
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