We consider fault-tolerant computation with formulas composed of noisy Boolean gates with two input wires. In our model all gates fail independently of each other and of the input. When a gate fails, it outputs the opposite of the correct output. It is known that if all gates fail with ... more >>>

It is well-known that the class of sets that can be computed by polynomial size circuits is equal to the class of sets that are polynomial time reducible to a sparse set. It is widely believed, but unfortunately up to now unproven, that there are sets in $EXP^{NP}$, or even ... more >>>

We prove a simple concentration inequality, which is an extension of the Chernoff bound and Hoeffding's inequality for binary random variables. Instead of assuming independence of the variables we use a slightly weaker condition, namely bounds on the co-moments.

This inequality allows us to simplify and strengthen several known ... more >>>