The paper provides a study of (minimalistic contextual) analysis by reduction. Inspired by the work of Solomon Marcus' and by categorial grammars we present a formal tool which represents categorial, contextual restarting automata and categorial, contextual, Marcus grammars at the same time.
Four types of (in)finite sets defined by these automata are considered as linguistically relevant. We have obtained several types of unbounded hierarchies for all four types of classes of languages considered here.