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An algebraic approach to reducing the number of variables of incompletely defined discrete functions

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Standard

An algebraic approach to reducing the number of variables of incompletely defined discrete functions. / Astola, Jaakko T.; Astola, Pekka; Stankovic, Radomir S.; Tabus, Ioan.

2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016. IEEE, 2016. s. 107-112.

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Harvard

Astola, JT, Astola, P, Stankovic, RS & Tabus, I 2016, An algebraic approach to reducing the number of variables of incompletely defined discrete functions. julkaisussa 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016. IEEE, Sivut 107-112, IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC, 1/01/00. https://doi.org/10.1109/ISMVL.2016.18

APA

Astola, J. T., Astola, P., Stankovic, R. S., & Tabus, I. (2016). An algebraic approach to reducing the number of variables of incompletely defined discrete functions. teoksessa 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016 (Sivut 107-112). IEEE. https://doi.org/10.1109/ISMVL.2016.18

Vancouver

Astola JT, Astola P, Stankovic RS, Tabus I. An algebraic approach to reducing the number of variables of incompletely defined discrete functions. julkaisussa 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016. IEEE. 2016. s. 107-112 https://doi.org/10.1109/ISMVL.2016.18

Author

Astola, Jaakko T. ; Astola, Pekka ; Stankovic, Radomir S. ; Tabus, Ioan. / An algebraic approach to reducing the number of variables of incompletely defined discrete functions. 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016. IEEE, 2016. Sivut 107-112

Bibtex - Lataa

@inproceedings{f0a5d8b36bcd4a30bb625be0a5c2e2a2,
title = "An algebraic approach to reducing the number of variables of incompletely defined discrete functions",
abstract = "In this paper, we consider incompletely defined discrete functions, i.e., Boolean and multiple-valued functions, f: S→ {0,1,,q - 1} where S ⊂ {0,1,,q - 1}n i.e., the function value is specified only on a certain subset S of the domain of the corresponding completely defined function. We assume the function to be sparse i.e. is 'small' relative to the cardinality of the domain. We show that by embedding the domain {0,1,,q - 1}n, where n is the number of variables and q is a prime power, in a suitable ring structure, the multiplicative structure of the ring can be used to construct a linear function {0,1,,q - 1}n → {0,1,,q - 1}m that is injective on S provided that m > 2logq|S|+logq(n - 1). In this way we find a linear transform that reduces the number of variables from n to m, and can be used e.g. in implementation of an incompletely defined discrete function by using linear decomposition.",
keywords = "index generation functions, multiple valued functions, reduction of variables",
author = "Astola, {Jaakko T.} and Pekka Astola and Stankovic, {Radomir S.} and Ioan Tabus",
note = "EXT={"}Stankovic, Radomir S.{"}",
year = "2016",
month = "7",
day = "18",
doi = "10.1109/ISMVL.2016.18",
language = "English",
publisher = "IEEE",
pages = "107--112",
booktitle = "2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016",

}

RIS (suitable for import to EndNote) - Lataa

TY - GEN

T1 - An algebraic approach to reducing the number of variables of incompletely defined discrete functions

AU - Astola, Jaakko T.

AU - Astola, Pekka

AU - Stankovic, Radomir S.

AU - Tabus, Ioan

N1 - EXT="Stankovic, Radomir S."

PY - 2016/7/18

Y1 - 2016/7/18

N2 - In this paper, we consider incompletely defined discrete functions, i.e., Boolean and multiple-valued functions, f: S→ {0,1,,q - 1} where S ⊂ {0,1,,q - 1}n i.e., the function value is specified only on a certain subset S of the domain of the corresponding completely defined function. We assume the function to be sparse i.e. is 'small' relative to the cardinality of the domain. We show that by embedding the domain {0,1,,q - 1}n, where n is the number of variables and q is a prime power, in a suitable ring structure, the multiplicative structure of the ring can be used to construct a linear function {0,1,,q - 1}n → {0,1,,q - 1}m that is injective on S provided that m > 2logq|S|+logq(n - 1). In this way we find a linear transform that reduces the number of variables from n to m, and can be used e.g. in implementation of an incompletely defined discrete function by using linear decomposition.

AB - In this paper, we consider incompletely defined discrete functions, i.e., Boolean and multiple-valued functions, f: S→ {0,1,,q - 1} where S ⊂ {0,1,,q - 1}n i.e., the function value is specified only on a certain subset S of the domain of the corresponding completely defined function. We assume the function to be sparse i.e. is 'small' relative to the cardinality of the domain. We show that by embedding the domain {0,1,,q - 1}n, where n is the number of variables and q is a prime power, in a suitable ring structure, the multiplicative structure of the ring can be used to construct a linear function {0,1,,q - 1}n → {0,1,,q - 1}m that is injective on S provided that m > 2logq|S|+logq(n - 1). In this way we find a linear transform that reduces the number of variables from n to m, and can be used e.g. in implementation of an incompletely defined discrete function by using linear decomposition.

KW - index generation functions

KW - multiple valued functions

KW - reduction of variables

U2 - 10.1109/ISMVL.2016.18

DO - 10.1109/ISMVL.2016.18

M3 - Conference contribution

SP - 107

EP - 112

BT - 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016

PB - IEEE

ER -