On computation of Boolean involutive bases

Authors:
V. P. Gerdt;M. V. Zinin;Yu. A. Blinkov
Affiliations:
Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Department of Mathematics and Mechanics, Saratov State University, Saratov, Russia 410071
Venue:
Programming and Computing Software
Year:
2010

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Abstract

Gröbner bases in Boolean rings can be calculated by an involutive algorithm based on the Janet or Pommaret division. The Pommaret division allows calculations immediately in the Boolean ring, whereas the Janet division implies use of a polynomial ring over field $$ \mathbb{F}_2 $$ . In this paper, both divisions are considered, and distributive and recursive representations of Boolean polynomials are compared from the point of view of calculation effectiveness. Results of computer experiments with both representations for an algorithm based on the Pommaret division and for lexicographical monomial order are presented.