We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP--hard problems are easier to solve. In particular, whether there exist algorithms that solve correctly ... more >>>

We present the first example of a natural distribution on instances of an NP-complete problem, with the following properties. With high probability a random formula from this distribution (a) is unsatisfiable, (b) has a short proof that can be found easily, and (c) does not have a short (general) resolution ... more >>>