A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials

Journal Article · Wed Oct 31 00:00:00 EDT 2012 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2012V203N10ABEH004270· OSTI ID:22094051

Gashkov, Sergey B; Sergeev, Igor' S ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

This work suggests a method for deriving lower bounds for the complexity of polynomials with positive real coefficients implemented by circuits of functional elements over the monotone arithmetic basis {l_brace}x+y, x {center_dot} y{r_brace} Union {l_brace}a {center_dot} x | a Element-Of R{sub +}{r_brace}. Using this method, several new results are obtained. In particular, we construct examples of polynomials of degree m-1 in each of the n variables with coefficients 0 and 1 having additive monotone complexity m{sup (1-o(1))n} and multiplicative monotone complexity m{sup (1/2-o(1))n} as m{sup n}{yields}{infinity}. In this form, the lower bounds derived here are sharp. Bibliography: 72 titles.

• OSTI ID: 22094051
• Journal Information: Sbornik. Mathematics, Vol. 203, Issue 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ADDITIVES
IMAGES
POLYNOMIALS