Switching functions whose monotone complexity is nearly quadratic

Monotone Complexity by Switching Lemma ∗

We prove a lower bound of 2 Ω (

Monotone, Horn and Quadratic Pseudo-Boolean Functions

A pseudo-Boolean function (pBf) is a mapping from f0; 1gn to the real numbers. It is known that pseudo-Boolean functions have polynomial representations, and it was recently shown that they also have disjunctive normal forms (DNFs). In this paper we relate the DNF syntax of the classes of monotone, quadratic and Horn pBfs to their characteristic inequalities.

The monotone circuit complexity of Boolean functions

Recently, Razborov obtained superpolynomial lower bounds for monotone circuits that lect cliques in graphs. In particular, Razborov showed that detecting cliques of size s in a graph dh m vertices requires monotone circuits of size .Q(m-'/(log m) ~') for fixed s, and size rn ao°~') for ,. :[log ml4J. In this paper we modify the arguments of Razborov to obtain exponential lower bounds for ,moton...

The Decision Tree Complexity for k-SUM is at most Nearly Quadratic

Following a recent improvement of Cardinal et al. [4] on the complexity of a linear decision tree for k-SUM, resulting in O(n log n) linear queries, we present a further improvement to O(n log n) such queries. Work on this paper by Esther Ezra has been supported by NSF CAREER under grant CCF:AF 1553354. Work on this paper by Micha Sharir was supported by Grant 892/13 from the Israel Science Fou...

Estimates on the Approximation of 3-monotone Functions by 3-monotone Quadratic Splines