Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
A Gro¨bner approach to involutive bases
Journal of Symbolic Computation
Sperner theory
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Groebner bases computation in Boolean rings for symbolic model checking
MOAS'07 Proceedings of the 18th conference on Proceedings of the 18th IASTED International Conference: modelling and simulation
Detecting unnecessary reductions in an involutive basis computation
Journal of Symbolic Computation
A Gröbner basis approach to CNF-formulae preprocessing
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
On compatibility of discrete relations
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
On connection between constructive involutive divisions and monomial orderings
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Role of involutive criteria in computing Boolean Gröbner bases
Programming and Computing Software
A Groebner bases-based approach to backward reasoning in rule based expert systems
Annals of Mathematics and Artificial Intelligence
On computation of Boolean involutive bases
Programming and Computing Software
Journal of Symbolic Computation
Journal of Symbolic Computation
Characteristic set algorithms for equation solving in finite fields
Journal of Symbolic Computation
Programming and Computing Software
Gröbner-free normal forms for Boolean polynomials
Journal of Symbolic Computation
A logic-algebraic approach to decision taking in a railway interlocking system
Annals of Mathematics and Artificial Intelligence
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In this paper an involutive algorithm for construction of Grobner bases in Boolean rings is presented. The algorithm exploits the Pommaret monomial division as an involutive division. In distinction to other approaches and due to special properties of Pommaret division the algorithm allows to perform the Grobner basis computation directly in a Boolean ring which can be defined as the quotient ring F2[x1,...,xn],12+x1,...,xn2+xn. Some related cardinality bounds for Pommaret and Grobner bases are derived. Efficiency of our first implementation of the algorithm is illustrated by a number of serial benchmarks.