Before revision:  In this work we  completely characterize the approximability of all Boolean CSPs in the streaming model . Specifically, given f, \gamma and \beta we show that either (1) the (\gamma,\beta)-approximation version of Max-CSP(f) has a probabilistic  streaming algorithm using O(\log n) space, or (2) for every \varepsilon > 0 the (\gamma-\varepsilon,\beta+\varepsilon)-approximation version of Max-CSP(f) requires \Omega(n) space for probabilistic  streaming algorithms.
After revision:  In this work we consider the approximability of Max-CSP(f) in the (dynamic) streaming setting, where constraints are inserted (and may also be deleted in the dynamic setting) one at a time. We completely characterize the approximability of all Boolean CSPs in the streaming model . Specifically, given f, \gamma and \beta we show that either (1) the (\gamma,\beta)-approximation version of Max-CSP(f) has a probabilistic streaming algorithm using O(\log n) space, or (2) for every \varepsilon > 0 the (\gamma-\varepsilon,\beta+\varepsilon)-approximation version of Max-CSP(f) requires \Omega(n) space for probabilistic streaming algorithms.