Church-Rosser languages and their application to parsing problems

Church-Rosser languages were defined by McNaughton, Narendran, and Otto in 1988. They are the deterministic variant of the growing context-sensitive languages. Their word problem is decidable in linear time and they are a propper superset of the deterministic context-free languages. Their definition is baes on confluent length-reducing string rewriting systems, enhanced by the possibility to mark word ends and to use variables (nonterminals). The thesis discusses the application of Church-Rosser languages to basic parsing problems, which, for example, appear in compiler construction. It is shown that it is possible to compute a description of each Church-Rosser language which has rewriting system fulfilling a special syntactical restriction. This restriction is similar to context-sensitive rules with swapped sides and ist called context-splittability. This result, which was not expected before, is a classification of the Church-Rosse languages which is also expandable to growing context-sensitive languages. For example, this normal form allows to compute syntax trees for accepted words of a Church-Rosser languages. Furthermore, it makes the proof easier that the Church-Rosser languages properly contain the deterministic context-free languages. Using this normal form a construction is introduced which can be used to describe certain the prefix languages of certain Church-Rosser languages again as Church-Rosser languages. Since in general this is not possible some decision problems arise. This are also discussed in the thesis, and at least paritally circumvented by test methods.