Copy Language and Dominance Formalisms

Got some new insight today when I looked at Shieber (1985) again: Swiss German is not weakly context-free, but the rationale is not that the copy language

ℒ_copy = { ww^R | w in {a,b}^* }

is not context-free like I wrongly remembered. The rationale is that the crossings language

ℒ_cross = { aⁿb^mcdⁿe^m | n, m ≥ 0 }

is not context-free.

Thus the argument that UVG-dl (Rambow, 1994) and DSG (Rambow et al., 2001) might not generate Swiss German does not hold for weak generation: the set of trees

   S             A               B
   |            / \            / | \
   A           a   A          b  B  e
   :               :
   A               C
   |              / \
   B             C   d
   :
   B
   |
   C
   :
   C
   |
   c

generates ℒ_cross. Of course, it is not linguistically adequate—it does not strongly generate the correct dependencies.