Abstract
We consider the problem of decomposing a positive DNF into a conjunction of DNFs, which may share a (possibly empty) given set of variables \(\varDelta \). This problem has interesting connections with traditional applications of positive DNFs, e.g., in game theory, and with the broad topic of minimization of boolean functions. We show that the finest \(\varDelta \)-decomposition components of a positive DNF can be computed in polynomial time and provide a decomposition algorithm based on factorization of multilinear boolean polynomials.
This work was supported by the grant of Russian Foundation for Basic Research No. 17-51-45125 and by the Ministry of Science and Education of the Russian Federation under the 5-100 Excellence Program.
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Notes
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A well–known heuristic optimizer based on the work of Brayton et al., which is often used as a reference tool for optimization of boolean functions.
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Ponomaryov, D. (2019). A Polynomial Time Delta-Decomposition Algorithm for Positive DNFs. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_28
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