Undecidable Properties on Length-Two String Rewriting Systems

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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.

Keywords

Rewriting system
confluence
left-most termination
right-most termination
length-two string rewriting system

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