Prefix languages of Church-Rosser languages

Church-Rosser languages are mainly based on confluent length reducing string rewriting systems. In general, the prefix language of a Church-Rosser language may not be describable by such a system, too. In this paper it is shown that under certain conditions it is possible to give a construction for a system defining the prefix language and to prove its correctness. The construction also gives a completion of prefixes to full words in the original language. This is an interesting property for practical applications, as it shows potential for error recovery strategies in parsers.