  The East model has a dynamical phase transition between an active (fluid) and
inactive (glass) state. We show that this phase transition generalizes to
"softened" systems where constraint violations are allowed with small but
finite probabilities. Moreover, we show that the first order coexistence line
separating the active and inactive phases terminates in a finite-temperature
space-time critical point. Implications of these results for equilibrium
dynamics are discussed.
