an:07154172
Zbl 1449.05018
Kauers, Manuel; Seidl, Martina; Zeilberger, Doron
On the maximal minimal cube lengths in distinct DNF tautologies
EN
DML, Discrete Math. Lett. 2, 47-51 (2019).
00444249
2019
j
05A15 68W30
covering systems; SAT solving; symmetry breaking
Summary: Inspired by a recent article by \textit{A. Zaleski} and \textit{D. Zeilberger} [``Boolean function analogs of covering systems'', Preprint, \url{arXiv:1801.05097}], we investigate the question of determining the largest \(k\) for which there exist Boolean formulas in disjunctive normal form (DNF) with \(n\) variables, which are tautologies, whose conjunctions have distinct sets of variables, and such that all the conjunctions have at leastkliterals. Using a SAT solver, we answer the question for some sizes which Zaleski and Zeilberger [loc. cit.] left open. We also determine the corresponding numbers for DNFs obeying certain symmetries.