An algebraic approach to reducing the number of variables of incompletely defined discrete functions
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Yksityiskohdat
| Alkuperäiskieli | Englanti |
|---|---|
| Otsikko | 2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016 |
| Kustantaja | IEEE |
| Sivut | 107-112 |
| Sivumäärä | 6 |
| ISBN (elektroninen) | 9781467394888 |
| DOI - pysyväislinkit | |
| Tila | Julkaistu - 18 heinäkuuta 2016 |
| OKM-julkaisutyyppi | A4 Artikkeli konferenssijulkaisussa |
| Tapahtuma | IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC - Kesto: 1 tammikuuta 1900 → … |
Julkaisusarja
| Nimi | |
|---|---|
| ISSN (elektroninen) | 2378-2226 |
Conference
| Conference | IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC |
|---|---|
| Ajanjakso | 1/01/00 → … |
Tiivistelmä
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.