Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Systems and software verification: model-checking techniques and tools
Systems and software verification: model-checking techniques and tools
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Gröbner-free normal forms for Boolean polynomials
Journal of Symbolic Computation
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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 Gröbner techniques have not been powerful enough to treat real-world applications. The proposed method avoids expensive Gröbner 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. 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 Gröbner basis computations.