Probably you should write $y[n]$ instead of $y(t)$. A strict memory-less system does not depend neither on past nor future values, only the current ones, to determine the current value of the output. The output at $n$ only depends on inputs at $n$.
By extension, some allow memory-less systems to allow a constant delay, i.e. to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ of a fixed integer $k$:
$y[n] = f(x[n-k])\,.$