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Zbl 0769.68041
Barrington, David A.Mix
Some problems involving Razborov-Smolensky polynomials. (English)
[A] Boolean function complexity, Sel. Pap. Symp., Durham/UK 1990, Lond. Math. Lect. Note Ser. 169, 109-128 (1992). ISBN 0-521-40826-1/pbk

Summary: [For the entire collection see Zbl 0754.00019.]\par Several recent results in circuit complexity theory have used a representation of Boolean functions by polynomials over finite fields. Our current inability to extend these results to superficially similar situations may be related to properties of these polynomials which do not extend to polynomials over general finite rings or finite abelian groups. Here we pose a number of conjectures on the behavior of such polynomials over rings and groups, and present some partial results toward proving them.

MSC 2000:: *68Q25 Analysis of algorithms and problem complexity
94C10 Switching theory
06E30 Boolean functions

Keywords: polynomials over groups; circuit complexity theory; representation of Boolean functions by polynomials; polynomials over rings

Citations: Zbl 0754.00019

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