Undecidable Properties on Length-Two String Rewriting Systems

Authors:
Masahiko Sakai;Yi Wang
Affiliations:
Graduate School of Information Science, Nagoya University, furo-cho Chikusa-ku, Nagoya 4648603 Japan;Graduate School of Arts and Science, The University of Tokyo, Komaba Meguro-ku, Tokyo 1538914 Japan
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

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Abstract

Length-two string rewriting systems are length-preserving string rewriting systems that consist of length-two rules. This paper shows that confluence, termination, left-most termination and right-most termination are undecidable properties for length-two string rewriting systems. These results mean that these properties are undecidable for the class of linear term rewriting systems in which depth-two variables are allowed in both sides of rules.