We consider the deterministic and the randomized decision tree complexities for Boolean functions, denoted DC(f) and RC(f), respectively. A major open problem is how small RC(f) ca...
We prove that the concept class of disjunctions cannot be pointwise approximated by linear combinations of any small set of arbitrary real-valued functions. That is, suppose there ...
We show that for k ≥ 3 even the Ω(n) level of the Lasserre hierarchy cannot disprove a random k-CSP instance over any predicate type implied by k-XOR constraints, for example ...
We study the problem of local search on a graph. Given a real-valued black-box function f on the graph's vertices, this is the problem of determining a local minimum of f--a v...
Many NP-hard problems can be solved efficiently when the input is restricted to graphs of bounded tree-width or clique-width. In particular, by the celebrated result of Courcelle,...
Fedor V. Fomin, Petr A. Golovach, Daniel Lokshtano...