Context-free grammar forms with strict interpretations

摘要

This paper begins a systematic investigation of context-free grammar forms using the mechanism of “strict” interpretations: the interpretations of terminal letters are defined exactly as those of nonterminal letters. Thus, strict interpretations are more closely related to the master grammar than the g-interpretations investigated in the original grammar form paper [A. Cremers and S. Ginsburg, Context-free grammar forms, J. Comput. System Sci. 11 (1975), 86–116]. The main results of this paper concern reducibility, closure properties, generators and hierarchies of language families, as well as the characterization of grammar forms generating (under strict interpretation) the families of regular and linear languages.