On the Implementation of Boolean Gröbner Bases

Shutaro Inoue () and Akira Nagai ()
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Shutaro Inoue: Tokyo University of Science
Akira Nagai: NTT Information Sharing Platform Laboratories

A chapter in Computer Mathematics, 2014, pp 87-92 from Springer

Abstract: Abstract We show how we can make Boolean Gröbner base computations feasible on standard computer algebra systems which have a routine to compute Gröbner bases in polynomial rings over the Galois field $$\mathbb {GF}_2$$ GF 2 . We also show that we can even compute a comprehensive Boolean Gröbner basis using only computations of Gröbner bases in a polynomial ring over $$\mathbb {GF}_2$$ GF 2 . Our implementation on the computer algebra system Risa/Asir achieves tremendous speedup compared with previous implementations of Boolean Gröbner bases.

Keywords: Standard Computer Algebra Systems; Boolean Polynomial Ring; Monomer Reduction; Sudoku Puzzle; Lazy Strategy (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-43799-5_8

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DOI: 10.1007/978-3-662-43799-5_8

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