Boolean Gröbner bases

Authors:
Yosuke Sato;Shutaro Inoue;Akira Suzuki;Katsusuke Nabeshima;Ko Sakai
Affiliations:
Department of Mathematical Information Science, Tokyo University of Science, Kagurazaka 1-3, Shinjuku-ku, Tokyo 162-8601, Japan;Department of Mathematical Information Science, Tokyo University of Science, Kagurazaka 1-3, Shinjuku-ku, Tokyo 162-8601, Japan;Graduate School of Science and Technology, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-8501, Japan;Institute of Socio-Arts and Sciences, The University of Tokushima, Minamijosanjima-cho 2-1, Tokushima 770-8506, Japan;Graduate School of Pure and Applied Sciences, University of Tsukuba, Tennodai 1-1-1, Tsukuba 305-8571, Japan
Venue:
Journal of Symbolic Computation
Year:
2011

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Abstract

In recent years, Boolean Grobner bases have attracted the attention of many researchers, mainly in connection with cryptography. Several sophisticated methods have been developed for the computation of Boolean Grobner bases. However, most of them only deal with Boolean polynomial rings over the simplest coefficient Boolean ring GF"2. Boolean Grobner 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 Grobner bases inspired us to return to their development. In this paper, we introduce our work on Boolean Grobner bases with arbitrary coefficient Boolean rings.