This paper shows that the languages over a one-letter alphabet generat
ed by context-free matrix grammars are always regular. Morover we give
a decision procedure for the question of whether a context-free matri
x language is finite. Hereby we strengthen a result of [Mk 92] and set
tle a number of open questions in [DP 89]. Both results are obtained b
y a reduction to Petri net problems.