Universal tests for memory words

The main result is a universal pointwise test that, when presented with a set of words $S$ on a finite or countable alphabet ${\cal X}$ that purports to be a set of memory words for a stationary process, will eventually almost surely return the value YES precisely when all positive probability words in $S$ are memory words. For example, if $S$ consists of all of the single letters in ${\cal X}$, then the test will eventually say yes if and only if the process is a Markov chain. Various further positive and negative results of this type are also given.