Some undecidable termination problems for semi-Thue systems

Word Problems and Confluence Problems for Restricted 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...

Decision Problems for Semi-Thue Systems with a Few Rules

For several decision problems about semi-Thue systems , we try to locate the frontier between the decidable and the undecidable from the point of view of the number of rules. We show that the the Termination Problem, the U-Termination Problem, the Accessibility Problem and the Common-Descendant Problem are undecidable for 3 rules STS. As a corollary we obtain the undecidability of the Post-Corr...

Notes on semi-Thue Systems

The main differences between symbolic and morphic formal systems: Instead of the Kleene star for the symbolic universes, morphic universes are generated by the Stirling cross. Symbolic substitution and concatenation is preserving production concatenation. Morphic substitution/concatenation is opening up a system of interactive complexions of derivations. Comparison of substitution based product...

Independent Instances for Some Undecidable Problems

— In this note we prove the existence of effectively independent instances (with respect to an arbitrary recursively axiomatizable, consistent, intuitively true and sufficiently rich theory) for some well-known undecidable problems including the Emptiness Problem, the Finiteness Problem, the Totality Problem, the Halting Problem and the Post Correspondence Problem. Applications in the Theory of...