On One-Rule Grid Semi-Thue Systems

Well Behaved Derivations in One-rule Semi-thue Systems

Termination of Single-Threaded One-Rule Semi-Thue Systems

This paper is a contribution to the long standing open problem of uniform termination of Semi-Thue Systems that consist of one rule s → t. McNaughton previously showed that rules incapable of (1) deleting t completely from both sides, (2) deleting t completely from the left, and (3) deleting t completely from the right, have a decidable uniform termination problem. We use a novel approach to sh...

On String Rewriting Systems

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 ...

On Termination of One Rule Rewrite Systems

The undecidability of the termination of rewrite systems is usually proved by reduction to the halting of Turing machines. In particular, Dauchet proves the unde-cidability of the termination of one rule rewrite systems by coding Turing machines into one rule rewrite systems. Rewrite systems are a very simple model of computation and one may expect proofs in this model to be more straightforwar...

Exploring Thue’s 1914 paper on the transformation of strings according to given rules

Reception of Thue’s Work Thue’s earlier work was not widely cited but often rediscovered independently [Hed67], and something similar seems to have happened with the 1914 paper. For example, Thue is not among the 547 authors in Church’s 1936 Bibliography of Symbolic Logic, nor is Thue cited in Post’s major work on tag systems, correspondence systems, or normal systems before 1947. His work appe...