Memorylessness

A system is memoryless if its output only depends on the current time, not past or future times. This is intuitively easy to understand. If a system depends on other values of time (like an integral or derivative), then it isn’t memoryless. i.e., the output value $y$ depends only on the input value $x$ at the same time $t$.

A CT LTI system is memoryless if and only if $\exists \alpha \in \mathbb{C}:h(t)=\alpha \delta (t)$. A DT LTI system is memoryless if and only if $\exists \alpha \in \mathbb{C}:h[n]=\alpha \delta [n]$.