Gröbner Bases for Boolean Function Minimization

• Main Authors: Faroß, Nicolas, Schwarz, Simon
• Other Authors: Universität des Saarlandes Saarbrücken, Max-Planck-Institut für Informatik (MPII), Max-Planck-Gesellschaft, Modeling and Verification of Distributed Algorithms and Systems (VERIDIS), Max-Planck-Gesellschaft-Max-Planck-Gesellschaft-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Formal Methods (LORIA - FM), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 1481
• Subjects: Multi-level Logic Optimization Boolean Function Synthesis Gröbner Bases; Multi-level Logic Optimization; Boolean Function Synthesis; Gröbner Bases; [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]; Tromsø
• Online Access: https://inria.hal.science/hal-04315477; https://inria.hal.science/hal-04315477/document; https://inria.hal.science/hal-04315477/file/short4.pdf

International audience 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.