Parsing Algorithms for Grammars with Regulated Rewriting

In recent papers [4, 5, 8, 11] Petri net controlled grammars have been introduced and investigated. It was shown that various regulated grammars such as random context, matrix, vector, valence grammars, etc., resulted from enriching context-free grammars with additional mechanisms can be unified into the Petri net formalism, i.e., a grammar and its control can be represented by a Petri net. This unification allows approaching the membership (parsing) problem in formal language theory in the new point of view: instead of a usual derivation tree, one can use a Petri net derivation tree in which the control mechanism is also considered as a part of the tree. In this paper, we show that the parsing problem for regulated grammars can be solved by means of Petri net derivation trees constructed using the net unfolding. Moreover, we present a parsing algorithm for the deterministic restriction of Petri net controlled grammars based on the well-known Earley parsing algorithm. Key–Words: Grammars with regulated rewriting, Petri nets, Petri net controlled grammars, Parsing algorithms