Complexity of Decision Problems on Totally Rigid Acyclic Tree Grammars

Totally rigid acyclic tree grammars (TRATGs) are an emerging grammatical formalism with numerous applications in proof theory and automated reasoning. We determine the computational complexity of several decision problems on TRATGs: membership, containment, disjointness, equivalence, minimization, and the complexity of minimal cover with a fixed number of nonterminals. We relate non-parametric minimal cover to a problem on regular word grammars of unknown complexity.