# 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:

- 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}

}

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