Boolean algebras of unambiguous context-free languages

Several recent works have studied subfamilies of deterministic context-free languages with good closure properties, for instance the families of input-driven or visibly pushdown languages, or more generally families of languages accepted by pushdown automata whose stack height can be uniquely determined by the input word read so far. These ideas can be described as a notion of synchronization. In this paper we present an extension of synchronization to all context-free languages using graph grammars. This generalization allows one to define boolean algebras of non-deterministic but unambiguous context-free languages containing regular languages