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hi so i want to talk about verifiers which is one of the most important things in uh complexity theory when we talk about non-deterministic languages of a certain type so what a verifier is is basically a way to verify whether some input is correct so um if you know what a clique is you can skip ahead a little bit but lets say that i have a graph right here lets say i have this one and lets make it a little bit more complicated so lets say we have this so a clique is or like if you prefer is a set of vertices that has every connection present uh among those vertices so a cake leak is a set of k vertices okay verts uh with all with all k choose two uh edges present among them so the question is like if we have a graph like this one here what kinds of cliques does it have and i can you can pretty easily see that there is a three click right here essentially a triangle because we have three vertices and all three edges are present between there are no more possible and you may wonder