Boolean Gröbner bases

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• 作者：Yosuke Sato^a ; ^{ysato@rs.kagu.tus.ac.jp} ; Shutaro Inoue^a ; ^{sinoue@rs.kagu.tus.ac.jp} ; Akira Suzuki^b ; ^{sakira@kobe-u.ac.jp} ; Katsusuke Nabeshima^c ; ^{nabesima@ias.tokushima-u.ac.jp} ; Ko Sakai^d ; ^{ksakai@math.tsukuba.ac.jp}
• 关键词：Boolean ring ; Grö ; bner bases ; Comprehensive Grö ; bner bases
• 刊名：Journal of Symbolic Computation
• 出版年：2011
• 出版时间：May 2011
• 年：2011
• 卷：46
• 期：5
• 页码：622-632
• 全文大小：281 K

文摘

In recent years, Boolean Gröbner bases have attracted the attention of many researchers, mainly in connection with cryptography. Several sophisticated methods have been developed for the computation of Boolean Gröbner bases. However, most of them only deal with Boolean polynomial rings over the simplest coefficient Boolean ring . Boolean Gröbner bases for arbitrary coefficient Boolean rings were first introduced by two of the authors almost two decades ago. While the work is not well-known among computer algebra researchers, recent active work on Boolean Gröbner bases inspired us to return to their development. In this paper, we introduce our work on Boolean Gröbner bases with arbitrary coefficient Boolean rings.