Comparing consecutive letter counts in multiple context-free languages

Abstract

Context-free grammars are not able to model cross-serial dependencies in natural languages. To overcome this issue, Seki et al. introduced a generalization called m-multiple context-free grammars (m-MCFGs), which deal with m-tuples of strings. We show that m-MCFGs are capable of comparing the number of consecutive occurrences of at most 2m different letters. In particular, the language {a n1 1 a n2 2 . . . a)-multiple context-free, but not m-multiple context-free. * Florian Lehner was supported by the FWF (Austrian Science Fund) project number J3850-N32 † C. Lindorfer was partially supported by Austrian Science Fund FWF P31237 and DK W1230.