Deterministic parsing for augmented context-free grammars

In contrast to the usual depth-first derivations of context-free (CF) grammars, breadth-first derivations (also in combination with depth-first ones) yield a class of augmented context-free grammars (ACF) (also termed multi-breadth-depth grammars) endowed with greater generative capacity, yet manageable. The inadequacy of CF grammars to treat distant dependencies is overcome by the new model. ACF grammars can be classified with respect to their disposition, a concept related to the data structure needed to parse their strings. For such augmented CF grammars we consider the LL(k) condition, that ensures top-down deterministic parsing. We restate the condition as an adjacency problem and we prove that it is decidable for any disposition. The deterministic linear-time parser differs from a recursive descent parser by using instead of a LIFO stack a more general data structure, involving FIFO queues and LIFO stacks in accordance with the disposition. ACF grammars can be also viewed as a formalized version of ATN (Augmented Transition Networks).