  In this paper, we study Reiter's propositional default logic when the
treewidth of a certain graph representation (semi-primal graph) of the input
theory is bounded. We establish a dynamic programming algorithm on tree
decompositions that decides whether a theory has a consistent stable extension
(Ext). Our algorithm can even be used to enumerate all generating defaults
(ExtEnum) that lead to stable extensions.
  We show that our algorithm decides Ext in linear time in the input theory and
triple exponential time in the treewidth (so-called fixed-parameter linear
algorithm).
  Further, our algorithm solves ExtEnum with a pre-computation step that is
linear in the input theory and triple exponential in the treewidth followed by
a linear delay to output solutions.
