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

Abstract

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.

Authors:
;  [1]
  1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22094051
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 203; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ADDITIVES; IMAGES; POLYNOMIALS

Citation Formats

Gashkov, Sergey B, and Sergeev, Igor' S. A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials. United States: N. p., 2012. Web. doi:10.1070/SM2012V203N10ABEH004270.
Gashkov, Sergey B, & Sergeev, Igor' S. A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials. United States. doi:10.1070/SM2012V203N10ABEH004270.
Gashkov, Sergey B, and Sergeev, Igor' S. Wed . "A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials". United States. doi:10.1070/SM2012V203N10ABEH004270.
@article{osti_22094051,
title = {A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials},
author = {Gashkov, Sergey B and Sergeev, Igor' S},
abstractNote = {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.},
doi = {10.1070/SM2012V203N10ABEH004270},
journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 10,
volume = 203,
place = {United States},
year = {2012},
month = {10}
}