$(m,n)$-rigid categorial grammars

In the article $(m,n)$-rigid categorial grammars are defined. An algorithm is proposed that verifies for a given grammar $G$ and natural numbers $m$, $n$ whether $G$ is $(m,n)$-rigid. It is proved that an infinite hierarchy exists in the class of $(m,n)$-rigid languages, and that the class of $(m,n)$-rigid grammars is incomparable with the class of regular languages. The complexity of the membership problem for $(m,n)$-rigid grammars is studied.