Preserving Regularity and Related Properties

A nite string-rewriting system R preserves regularity if and only if it preserves-regularity, where is the alphabet containing exactly those letters that have occurrences in the rules of R. This proves a conjecture of Gyenizse and VV agvv olgyi (1995). In addition, some undecidability results are presented that generalize some results of Gilleron and Ti-son (1995) from term-rewriting systems to string-rewriting systems. In particular, it is shown that it is undecidable in general whether a nite, length-reducing, and connuent string-rewriting system yields a regular set of normal forms for each regular language.