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We introduce a notion of the quantum query complexity of a certificate structure. This is a formalization of a well-known observation that many quantum query algorithms only require the knowledge of the position of possible certificates in the input string, not the precise values therein. Next, we derive a dual formulation of the complexity of a non-adaptive learning graph and use it to show that non-adaptive learning graphs are tight for all certificate structures. By this, we mean that theredoi:10.1109/ccc.2013.14 dblp:conf/coco/BelovsR13 fatcat:wzeax7k42jfqnesi2nbnr65seq