Abstract. We show that every monotone formula that computes the threshold function THk, n, 2⩽k⩽n/2, has size at least ⌊k/2⌋ n log(n/(k−1)). The same lower bound ...
Their complexity has been studied in various circuit models. In this paper, we show lower bounds on the size of monotone formulas computing threshold functions.
Aug 29, 2011 · We show that every monotone formula that computes the threshold function THk, n, 2≤ , k≤n/2, has size at least ⌊k/2⌋ n log(n/(k−1)). The same ...
Jan 11, 2011 · Nothing better than super-polynomial is known for matching. Raz has a result that monotone circuits for matching have linear depth. (Thanks ...
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lower bounds on the size of monotone formulas com- puting Th. Let LM(T) be the minimum size of a monotone formula computing T. It is easy to see that LM(T) ...
Nov 21, 2016 · Even if we restrict ourselves to monotone formulas, the best known lower bounds are of the form. 2Ω(n/ log n) for a function computable in NP ...
Abstract. We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, ...
Nov 9, 2020 · For any unsatisfiable CNF formula F that is hard to refute in the Resolution proof system, we show that a gadget-composed version of F is hard ...
Lower bounds for monotone counting circuits - ScienceDirect.com
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Nov 20, 2016 · Then we have n d ≤ C ( f A ) ≤ n d + 1 , where the upper bound is trivial, and the lower bound follows from Corollary 2. Thus, for polynomials ...
Even if we restrict ourselves to monotone formulas, the best known lower bounds are of the form 2Ω(n/ log n) for a function computable in NP [12], which is ...