  Context-free languages can be characterized in several ways. This article
studies projective linearisations of languages of simple dependency trees,
i.e., dependency trees in which a node can govern at most one node with a given
syntactic function. We prove that the projective linearisations of local
languages of simple dependency trees coincide with the context-free languages.
  Simple dependency trees suggest alternative dual notions of locality and
projectivity, which permits defining a dual language for each context-free
language. We call this new class of languages anti-context-free. These
languages are related to some linguistic constructions exhibiting the so-called
cross-serial dependencies that were historically important for the development
of computational linguistics. We propose that this duality could be a relevant
linguistic phenomenon.
