  We define a decidable class of TAGs that is strongly equivalent to CFGs and
is cubic-time parsable. This class serves to lexicalize CFGs in the same manner
as the LCFGs of Schabes and Waters but with considerably less restriction on
the form of the grammars. The class provides a normal form for TAGs that
generate local sets in much the same way that regular grammars provide a normal
form for CFGs that generate regular sets.
