  We study propagation of the RegularGcc global constraint. This ensures that
each row of a matrix of decision variables satisfies a Regular constraint, and
each column satisfies a Gcc constraint. On the negative side, we prove that
propagation is NP-hard even under some strong restrictions (e.g. just 3 values,
just 4 states in the automaton, or just 5 columns to the matrix). On the
positive side, we identify two cases where propagation is fixed parameter
tractable. In addition, we show how to improve propagation over a simple
decomposition into separate Regular and Gcc constraints by identifying some
necessary but insufficient conditions for a solution. We enforce these
conditions with some additional weighted row automata. Experimental results
demonstrate the potential of these methods on some standard benchmark problems.
