Sequentially Indexed Grammars

This paper defines the grammar class of sequentially indexed grammars. Sequentially indexed grammars are the result of a change in the index stack handling mechanism of indexed grammars [Aho68, Aho69]. Sequentially indexed grammars are different from linear indexed grammars [Gaz88]. Like indexed languages, sequentially indexed languages are a fully abstract language class. Unlike indexed languages, sequentially indexed languages allow polynomial parsing algorithms. We give a polynomial algorithm for parsing with sequentially indexed gramamrs that is an extension of the Earley algorithm for parsing with context free grammars.