On the size of irredundant propagation complete CNF formulas

09/04/2023

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by   Petr Savický, et al.

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We investigate propagation complete (PC) CNF formulas for a symmetric definite Horn function of n variables and demonstrate that the minimum size of these formulas is closely related to specific covering numbers, namely, to the smallest number of k-subsets of an n-set covering all (k-1)-subsets for a suitable k. As a consequence, we demonstrate an irredundant PC formula whose size is larger than the size of a smallest PC formula for the same function by a factor Ω(n/ln n). This complements a known polynomial upper bound on this factor.