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The behavior of a quantum system depends on how it is measured. How much of what is observed comes from the structure of the quantum system itself and how much from the observer's choice of measurement? We explore these questions by analyzing the language diversity of quantum finite-state generators. One result is a new way to distinguish quantum devices from their classical (stochastic) counterparts. While the diversity of languages generated by these two computational classes is the same inarXiv:quant-ph/0611203v1 fatcat:zteu62ubcbb2rkh6blwj7zyifu