  We investigate conjunctive normal form (CNF) encodings of a function
represented with a decomposable negation normal form (DNNF). Several encodings
of DNNFs and decision diagrams were considered by (Abio et al. 2016). The
authors differentiate between encodings which implement consistency or domain
consistency by unit propagation from encodings which are unit refutation
complete or propagation complete. The difference is that in the former case we
do not care about propagation strength of the encoding with respect to the
auxiliary variables while in the latter case we treat all variables (the main
and the auxiliary ones) in the same way. The currently known encodings of DNNF
theories implement domain consistency. Building on these encodings we
generalize the result of (Abio et al. 2016) on a propagation complete encoding
of decision diagrams and present a propagation complete encoding of a DNNF and
its generalization for variables with finite domains.
