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Testing Flavor Symmetries by B-Factory

Predictions of the Cabibbo-Kobayashi-Maskawa (CKM) parameters are investigated in detail in recent predictive models which are based on low-energy non-abelian discrete family symmetries. Some of the models can already be excluded at the present precision of the determination of the CKM parameters, while some of them seem to survive. We find that to make the uncertainties in the predictions comparable with the assumed uncertainties of $\sim 1^{\circ}$ and $\sim 2^{\circ}$ in $ϕ_2$ and $ϕ_3$, respectively, at about 50 inverse atto barn achieved at a feature B factory, it is necessary to reduce the uncertainties in the quark masses, especially that of the strange quark mass by more than 60%.