We show that derandomizing Polynomial Identity Testing is,
essentially, equivalent to proving circuit lower bounds for
NEXP. More precisely, we prove that if one can test in polynomial
time (or, even, nondeterministic subexponential time, infinitely
often) whether a given arithmetic circuit over integers computes an
identically zero polynomial, then either ... more >>>

Decision trees are representations of discrete functions with widespread applications in, e.g., complexity theory and data mining and exploration. In these areas it is important to obtain decision trees of small size. The minimization problem for decision trees is known to be NP-hard. In this paper the problem is shown ... more >>>

By the breakthrough work of Håstad, several constraint satisfaction
problems are now known to have the following approximation resistance
property: satisfying more clauses than what picking a random
assignment would achieve is NP-hard. This is the case for example for
Max E3-Sat, Max E3-Lin and Max E4-Set Splitting. A notable ... more >>>