On Regularity-Preservation by String-Rewriting Systems

Authors:
Peter Leupold
Affiliations:
Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Kyoto, Japan 603-8555
Venue:
Language and Automata Theory and Applications
Year:
2008

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Abstract

When using string-rewriting systems in the context of formal languages, one of the most common questions is whether they preserve regularity. A class of string-rewriting systems that has received attention lately are idempotency relations. They were mainly used to generate languages starting from a single word.Here we apply these relations to entire languages and investigate whether they preserve regularity. For this, it turns out to be convenient to define two more general classes of string-rewriting systems, the k-period expanding and the k-period reducing ones. We show that both preserve regularity. This implies regularity preservation for many classes of idempotency relations.