  This work concerns formal descriptions of DNA code properties, and builds on
previous work on transducer descriptions of classic code properties and on
trajectory descriptions of DNA code properties. This line of research allows us
to give a property as input to an algorithm, in addition to any regular
language, which can then answer questions about the language and the property.
Here we define DNA code properties via transducers and show that this method is
strictly more expressive than that of trajectories, without sacrificing the
efficiency of deciding the satisfaction question. We also show that the
maximality question can be undecidable. Our undecidability results hold not
only for the fixed DNA involution but also for any fixed antimorphic
permutation. Moreover, we also show the undecidability of the antimorphic
version of the Post Corresponding Problem, for any fixed antimorphic
permutation.
