Phrase-Structure Grammars: Normal Forms and Reduction

This paper establishes two new normal forms for phrase-structure grammars in which both context-free rules and non-context-free rules are in prescribed forms. In addition, a limit is placed on the number of context-free rules. More specifically, the first form has 2 + n context-free rules, where n is the number of terminals. Concerning non-context-free rules, each of them has the form AB -> CD, where A, B, C, D are nonterminals. The second normal form has always only two context-free rules---S -> S# and # -> e, where S is the start symbol, # is a nonterminal, and e is the empty string. Regarding non-context-free rules, each of them is of the form AB -> XD, where A, B, D are nonterminals and X is a nonterminal or a terminal.