  In this paper we consider the problem of computing an mRNA sequence of
maximal similarity for a given mRNA of secondary structure constraints,
introduced by Backofen et al. in [BNS02] denoted as the MRSO problem. The
problem is known to be NP-complete for planar associated implied structure
graphs of vertex degree at most 3. In [BFHV05] a first polynomial dynamic
programming algorithms for MRSO on implied structure graphs with maximum vertex
degree 3 of bounded cut-width is shown. We give a simple but more general
polynomial dynamic programming solution for the MRSO problem for associated
implied structure graphs of bounded clique-width. Our result implies that MRSO
is polynomial for graphs of bounded tree-width, co-graphs, $P_4$-sparse graphs,
and distance hereditary graphs. Further we conclude that the problem of
comparing two solutions for MRSO is hard for the class of problems which can be
solved in polynomial time with a number of parallel queries to an oracle in NP.
