A Polynomial Parser for Contextual Grammars with Linear, Regular and Context{Free Selectors

Contextual Grammars were introduced by Solomon Marcus in 1969 as \intrinsic grammars" without auxiliary symbols, based only on the fundamental linguistic operation of inserting words into given phrases according to certain contextual dependencies. The formal properties of the formalism have been extensively studied. Furthermore, it can be shown that this formalism provides an appropriate description of natural languages. But unfortunately, up to now no parser which runs in polynomial time was known for some linguistically relevant classes of Contextual Grammar. In the following, an intertwined two{level Earley{ based parser is presented for Contextual Grammars with nite, regular or context{free selectors on the basis of the three derivation deenitions in, Mg and Ml, i.e. the unrestricted replacement of contexts according to a selector, only allowing the replacement of maximal selectors according to all selectors or according to the same selector. The individual two passes can be characterized as follows. In the rst phase, all contexts to the left and right of its selector and all selector strings in a given input string are identiied and stored in items denoting the left and right boundary of the analysed input. These fragments are used in the second phase in order to check the context{free rules (sel i ?! The two phases are intertwined by repeatingly predicting new contexts and selectors for each removed context in the input string and accordingly identifying new context{selector pairs. Here it is important to note that the newly provided input reuses all currently produced items. The algorithm accepts ii in the item list I n (n = length of the input string)