An infinite hierarchy of language families generated by scattered context grammars with n-limited derivations

Authors:
Alexander Meduna;Jií Techet
Affiliations:
Department of Information Systems, Faculty of Information Technology, Brno University of Technology, Boetchova 2, Brno 61266, Czech Republic;Department of Information Systems, Faculty of Information Technology, Brno University of Technology, Boetchova 2, Brno 61266, Czech Republic
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

This paper introduces scattered context grammars without erasing productions, in which an application of a production always occurs within the first n nonterminals of the current sentential form. It demonstrates that this restriction gives rise to an infinite hierarchy of language families each of which is properly included in the family of context-sensitive languages. In addition, it proves analogous results for unordered scattered context grammars. Some consequences of these results are derived and open problems formulated.