# On the Depth of k-Valued Logic Functions Over Arbitrary Bases

## Abstract

The behavior of the Shannon function of the depth of k-valued logic functions realized by circuits over an arbitrary complete basis is examined. For all k, k ≥ 3, for an arbitrary basis of k-valued logic functions, the existence of the asymptotic behavior of the Shannon function of the depth is established. The asymptotic behavior is linear for finite bases and it is constant or logarithmic for infinite bases. Thus, the complete picture of asymptotic behavior of the Shannon function of the depth is obtained for all k, k ≥ 2.

- Authors:

- Keldysh Institute of Applied Mathematics (Russian Academy of Sciences) (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22773911

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 233; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; FUNCTIONS; MATHEMATICAL LOGIC

### Citation Formats

```
Kochergin, A. V., E-mail: alexeykoch@mail.ru.
```*On the Depth of k-Valued Logic Functions Over Arbitrary Bases*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3927-5.

```
Kochergin, A. V., E-mail: alexeykoch@mail.ru.
```*On the Depth of k-Valued Logic Functions Over Arbitrary Bases*. United States. doi:10.1007/S10958-018-3927-5.

```
Kochergin, A. V., E-mail: alexeykoch@mail.ru. Wed .
"On the Depth of k-Valued Logic Functions Over Arbitrary Bases". United States. doi:10.1007/S10958-018-3927-5.
```

```
@article{osti_22773911,
```

title = {On the Depth of k-Valued Logic Functions Over Arbitrary Bases},

author = {Kochergin, A. V., E-mail: alexeykoch@mail.ru},

abstractNote = {The behavior of the Shannon function of the depth of k-valued logic functions realized by circuits over an arbitrary complete basis is examined. For all k, k ≥ 3, for an arbitrary basis of k-valued logic functions, the existence of the asymptotic behavior of the Shannon function of the depth is established. The asymptotic behavior is linear for finite bases and it is constant or logarithmic for infinite bases. Thus, the complete picture of asymptotic behavior of the Shannon function of the depth is obtained for all k, k ≥ 2.},

doi = {10.1007/S10958-018-3927-5},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 233,

place = {United States},

year = {2018},

month = {8}

}

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