design problem so you prove a lower bound circuit lower bound if and only if you desire test data for testing whether a given function of given circuit computes a particular function okay so trying to minimize the test data you need to test whether a circuit computes of function is actually equivalent to proving a lower bound so this is very nice in the sense that that it gives a very constructive way of thinking about how you prove an impossibility result a very algorithmic way how you do and so in general I think we will make serious