  We investigate temporal correlations in the simplest measurement scenario,
i.e., that of a physical system on which the same measurement is performed at
different times, producing a sequence of dichotomic outcomes. The resource for
generating such sequences is the internal dimension, or memory, of the system.
We characterize the minimum memory requirements for sequences to be obtained
deterministically, and numerically investigate the probabilistic behavior below
this memory threshold, in both classical and quantum scenarios. A particular
class of sequences is found to offer an upper-bound for all other sequences,
which suggests a nontrivial universal upper-bound of $1/e$ for the classical
probability of realization of any sequence below this memory threshold. We
further present evidence that no such nontrivial bound exists in the quantum
case.
