Church-Rosser Groups and Growing Context-Sensitive Groups

A finitely generated group is called a Church-Rosser group (growing contextsensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the ChurchRosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free languages. As each contextfree 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-contextfree 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