New frontiers beyond context-freeness: DI-grammars and DI-automata

Authors:
Peter Staudacher
Affiliations:
Universität Regensburg, Regensburgh, Germany
Venue:
EACL '93 Proceedings of the sixth conference on European chapter of the Association for Computational Linguistics
Year:
1993

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Abstract

A new class of formal languages will be defined - the Distributed Index Languages (DI-languages). The grammar-formalism generating the new class - the DI-grammars - cover unbound dependencies in a rather natural way. The place of DI-languages in the Chomsky-hierarchy will be determined: Like Aho's indexed Languages, DI-languages represent a proper subclass of Type 1 (contextsensitive languages) and properly include Type 2 (context-free languages), but the DI-class is neither a subclass nor a superclass of Aho's indexed class. It will be shown that, apart from DI-grammars, DI-languages can equivalently be characterized by a special type of automata - DI-automata. Finally, the time complexity of the recognition-problem for an interesting subclass of DI-Grammars will approximately be determined.