General grammars that generate their sentences through derivation trees satisfying certain restrictions can be shown to generate k-linear or regular languages.
The languages recognized by higher-dimensional automata are precisely the rational subsumption-closed sets of finite interval pomsets.
Affine string-to-string functions definable in the planar affine λ-calculus λ℘ and first-order string transductions coincide.
The languages of higher-dimensional automata (HDAs) are precisely the subsumption closures of monadic second-order (MSO) definable sets of interval ipomsets of bounded width.