Church-Rosser groups and growing context-sensitive groups

  • Authors:

  • Mark Kambites;Friedrich Otto

  • Affiliations:

  • School of Mathematics, University of Manchester, Manchester, England;Fachbereich Elektrotechnik/Informatik, Universität Kassel, Kassel, Germany

  • Venue:
  • Journal of Automata, Languages and Combinatorics
  • Year:
  • 2008

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Abstract

A finitely generated group is called a Church-Rosser group (growing context-sensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the Church-Rosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free languages. As each context-free group language is actually deterministic context-free, it follows that all context-free groups are Church-Rosser groups. As the free abelian group of rank 2 is a non-context-free Church-Rosser group, this inclusion is proper. On the other hand, we show that there are co-context-free groups that are not growing context-sensitive. Also some closure and non-closure properties are established for the classes of Church-Rosser and growing context-sensitive groups. More generally, we also establish some new characterizations and closure properties for the classes of Church-Rosser and growing context-sensitive languages.