Thue systems as rewriting systems

This paper is a survey of recent results on Thue systems, where the systems are viewed as rewriting systems on strings over a finite alphabet. The emphasis is on Thue systems with the Church-Rosser property, where the notion of reduction is based on length-decreasing rewriting rules. The main effort is expended in outlining the properties of such systems, paying close attention to the issue of the possible decidability of properties and to the issue of the computational complexity of decidable properties. Since Thue systems may also be considered as presentations of monoids, the language of monoids (and groups) is used to describe some of these properties.

The word problem for free partially commutative groups

On deciding the confluence of a finite string-rewriting system on a given congruence class

In recent years a number of conditions have been established that a monoid must necessarily satisfy if it is to have a presentation through some finite convergent string-rewriting system. Here we give a survey on this development, explaining these necessary conditions in detail and describing the relationships between them.

Properties of Monoids That Are Presented by Finite Convergent String-Rewriting Systems — A Survey

An O(|T|3) algorithm for testing the Church-Rosser property of thue systems

The undecidability of the preperfectness of thue systems

and can easily be seen to be undecidable in the general case. Therefore, previous work has focused on identifying specic conditions and methods in which the problem is decidable. We continue the investigation in this paper, building on previous combination results, [2, 4, 7] and [6]. We are able to develop a novel approach to the non-disjoint combination problem. The approach is based on a new set of restrictions and combination method such that if the restrictions are satised the method produces an algorithm for the unication problem in the union of non-disjoint equational theories.

Paliath Narendran

Papers

An O(|T|3) algorithm for testing the Church-Rosser property of thue systems

The undecidability of the preperfectness of thue systems

Hierarchical Combination of Unication Algorithms (Extended Abstract).

Hierarchical Combination of Matching