Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Relations between roots and coefficients, interpolation and application to system solving
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Gröbner-free normal forms for boolean polynomials
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
A pommaret division algorithm for computing Grobner bases in boolean rings
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials
Journal of Symbolic Computation
Systems and Software Verification: Model-Checking Techniques and Tools
Systems and Software Verification: Model-Checking Techniques and Tools
Efficient computation of algebraic immunity for algebraic and fast algebraic attacks
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Hierarchical Verification of Galois Field Circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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This paper introduces a new method for interpolation of Boolean functions using Boolean polynomials. It was motivated by some problems arising from computational biology, for reverse engineering the structure of mechanisms in gene regulatory networks. For this purpose polynomial expressions have to be generated, which match known state combinations observed during experiments. Earlier approaches using Grobner techniques have not been powerful enough to treat real-world applications. The proposed method avoids expensive Grobner basis computations completely by directly calculating reduced normal forms. The problem statement can be described by Boolean polynomials, i.e. polynomials with coefficients in {0,1} and a degree bound of one for each variable. Therefore, the reference implementations mentioned in this work are built on the top of the PolyBoRi framework, which has been designed exclusively for the treatment of this special class of polynomials. A series of randomly generated examples is used to demonstrate the performance of the direct method. It is also compared with other approaches, which incorporate Grobner basis computations.