First-Order Logic Definability of Free Languages

Operator Precedence Grammars (OPGs) define a deterministic class of context-free languages, which extend input-driven languages and still enjoy many properties: they are closed w.r.t. Boolean operations, concatenation and Kleene star; the emptiness problem is decidable; they are recognized by a suitable model of pushdown automaton; they can be characterized in terms of a monadic second-order logic. Also, they admit efficient parallel parsing.