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Conference Papers Year : 2024

Gröbner Bases for Boolean Function Minimization

Abstract

Boolean function minimization techniques try to find, for a given formula, a smaller equivalent formula. In this work, we present a novel technique for heuristic boolean function minimization. By using an algebraic encoding, we embed the minimization problem into an algebraic domain, where algorithms for computing Gröbner bases are applicable. A Gröbner basis usually forms a compact representation of our encoded function. From the Gröbner basis, we then reconstruct an equivalent, more compact boolean formula. Our approach is the first to use Gröbner bases for function minimization. Combined with advances of algebraic Gröbner bases in satisfiability checking, this motivates further research on applications of Gröbner bases in the context of boolean logic.
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hal-04315477 , version 1 (30-11-2023)

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  • HAL Id : hal-04315477 , version 1

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Nicolas Faroß, Simon Schwarz. Gröbner Bases for Boolean Function Minimization. Proceedings of the 8th SC-Square Workshop, Jul 2024, Tromsø, Norway. ⟨hal-04315477⟩
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