Abstract
We give an answer to a question of Barrington, Beigel and Rudich, asked in 1992, concerning the largest n such that the OR function in n variables can be weakly represented by a quadratic polynomial modulo 6. More specifically, we show that no 11-variable quadratic polynomial exists that is congruent to zero modulo 6 if all arguments are 0, and non-zero modulo 6 on the set {0,1}, otherwise.
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Mix Barrington, D.A., Beigel, R., Rudich, S.: Representing boolean functions as polynomials modulo composite numbers (extended abstract). In: STOC, pp. 455–461. ACM Press, New York (1992)
Erdős, P.: Some remarks on the theory of graphs. Bull. Am. Math. Soc. 53, 292–294 (1947)
Grolmusz, V.: Superpolynomial size set-systems with restricted intersections mod 6 and explicit ramsey graphs. Combinatorica 20(1), 71–86 (2000)
Smolensky, R.: Algebraic methods in the theory of lower bounds for boolean circuit complexity. In: STOC, pp. 77–82. ACM, New York (1987)
Tardos, G., Mix Barrington, D.A.: A lower bound on the mod 6 degree of the or function. In: ISTCS, pp. 52–56 (1995)
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© 2007 Springer-Verlag Berlin Heidelberg
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Győr, G. (2007). Representing the Boolean OR Function by Quadratic Polynomials Modulo 6. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_28
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DOI: https://doi.org/10.1007/978-3-540-74240-1_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74239-5
Online ISBN: 978-3-540-74240-1
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