Comparing consecutive letter counts in multiple context-free languages

Context-free grammars are not able to capture cross-serial dependencies occurring in some 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 ₁ ^{n ₁} a ₂ ^{n ₂} ⋯a _2m+1 ^{n _2m+1} |n ₁≥n ₂≥…≥n _2m+1≥0} is (m+1)-multiple context-free, but not m-multiple context-free.