Polynomial Bounded Proof Complexities for Some Classes of DNF-Tautologies - Petrosyan, Garik (Mathematical Problems of Computer Science, 2020)
In this paper, we present the results on Frege proof complexities of some DNFtautologies. At first we introduce the notion of complete DNFs and prove that complete DNFs are tautologies, we also show that if the proof complexities for the set of complete DNFs are polynomially bounded, then the set of DNF-tautologies D, for which the number of non-negated variables in every conjunct is O(log(D)), also has polynomially bounded proof complexities. Later we show that the set of all balanced DNF-tautologies has polynomial proof complexities..