An anti-causal system is just a little bit modified version of a non-causal system. The system depends upon the future values of the input only. It has no dependency either on present or on the past values.
Find out whether the following systems are anti-causal.
a) $y(t) = x(t)+x(t-1)$
The system has two sub-functions. One sub function x(t+1) depends on the future value of the input but another sub-function x(t) depends only on the present. As the system is dependent on the present value also in addition to future value, this system is not anti-causal.
b) $y(t) = x(t+3)$
If we analyze the above system, we can see that the system depends only on the future values of the system i.e. if we put t = 0, it will reduce to x(3), which is a future value. This system is a perfect example of anti-causal system.