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Is their a relationship between non-causality and memory?

for example: is the system $Y(t) = X(t+1)$ memory or memory-less.

I got confused because the memory system is defined to depend only on the (same time) input, when the memory-less depends on the past, but nobody talk about the future.

thanks in advance.

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The output of a memoryless system depends only on the current input. All other systems have memory. For a non-causal system you need to "remember the future" in order to be able to compute the current output.

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