Some undecidability results concerning the property of preserving regularity

Friedrich Otto
1998 Theoretical Computer Science  
A finite string-rewriting system R preserves regularity if and only if it preserves Z-regularity, where C is the alphabet containing exactly those letters that have occurrences in the rules of R. This proves a conjecture of Gyenizse and Vigvijlgyi (1997). In addition, some undecidability results are presented that generalize results of Gilleron and Tison (1995) from term-rewriting systems to string-rewriting systems. It follows that the property of being regularity preserving is undecidable for
more » ... term-rewriting systems, thus answering another question of Gyenizse and VBgviilgyi (1997). Finally, it is shown that it is undecidable in general whether a finite, lengthreducing, and confluent string-rewriting system yields a regular set of normal forms for each regular language. @ 1998-Elsevier Science B.V. All rights reserved
doi:10.1016/s0304-3975(98)00055-3 fatcat:ighxqdcmazhzbm4v7pxenpq7wu