We associate a CNF-formula to every instance of the mean-payoff game problem in such a way that if the value of the game is non-negative the formula is satisfiable, and if the value of the game is negative the formula has a polynomial-size refutation in $\Sigma_2$-Frege (i.e.~DNF-resolution). This reduces mean-payoff ... more >>>

A long standing open problem in the computational complexity theory
is to separate NE from BPP, which is a subclass of $NP_T (NP\cap P/poly)$.
In this paper, we show that $NE\not\subseteq NP_T (NP \cap$ Nonexponentially-Dense-Class),
where Nonexponentially-Dense-Class is the class of languages A without exponential density
(for ... more >>>

We settle a number of questions in variants of Winfree's abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the "hierarchical" aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the "seeded" aTAM, tiles attach one at a time to a ... more >>>