On String Rewriting Systems
نویسنده
چکیده
String rewriting systems, also known as semi-Thue systems, consist of a set of rules l → r, specifying valid replacements of substrings of strings over a given alphabet. In the case of one single rule, it is an open problem whether there is a system that is neither terminating nor looping. Another open question is the decidability of termination. Difficulties arise especially for non-confluent systems. In this article, we develop strategies for approaching non-confluent string rewriting in general, not necessarily requiring only one rule. For a given system, we define an equivalent system with confluence-like properties, enabling us to develop some normal form theorems. Subsequently, we apply our methods to present a partial solution to the first of the mentioned problems, going one step further than Geser’s previous result by only requiring that there is a unique overlap in one order, but not making any restrictions for the other order. However, one case, where the right side is mainly periodic with a very special period, remains open. We further discuss implications for the latter question. We believe that our approach can be used to attack other questions in the subject of string rewriting.
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تاریخ انتشار 2012