String-rewriting systems
Handbook of formal languages, vol. 1
Some undecidability results concerning the property of preserving regularity
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
Journal of the ACM (JACM)
Proving termination with multiset orderings
Communications of the ACM
Tree Automata and Term Rewrite Systems
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Deleting string rewriting systems preserve regularity
Theoretical Computer Science - Developments in language theory
Regularity and context-freeness over word rewriting systems
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Finding finite automata that certify termination of string rewriting
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
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A string rewriting system R is called deleting if there exists a partial ordering on its alphabet such that each letter in the right hand side of a rule is less than some letter in the corresponding left hand side. We show that the rewrite relation R* induced by R can be represented as the composition of a finite substitution (into an extended alphabet), a rewrite relation of an inverse context-free system (over the extended alphabet), and a restriction (to the original alphabet). Here, a system is called inverse context-free if |r| ≤ 1 for each rule l → r. The decomposition result directly implies that deleting systems preserve regularity, and that inverse deleting systems preserve context-freeness. The latter result was already obtained by Hibbard [Hib74].