  A generic formalism is presented for the time-dependent or time-integrated
decays of any coherent $P^{0}\bar{P}^{0}$ system ($P^{0} = K^{0}, D^{0},
B^{0}_{d}$, or $B^{0}_{s}$). To meet various possible measurements at
asymmetric $B$ factories, we reanalyze some typical signals of CP violation in
the coherent $B^{0}_{d}\bar{B}^ {0}_{d}$ transitions. The advantage of proper
time cuts is illustrated for measuring mixing parameters and CP violation. We
show that the direct and indirect CP asymmetries are distinguishable in neutral
B decays to CP eigenstates. The possibility to detect the CP- forbidden
processes at the $\Upsilon (4S)$ resonance is explored in some detail.
