Some Undecidability Results for Non-Monadic Church-Rosser Thue Systems

Abstract In this paper the ‘computational power’ of finite Church-Rosser Thue systems that are non-monadic is explored. In particular, it is shown that there exists a finite non-monadic Church-Rosser Thue system T such that the set of linear sentences that are true under the interpretation given by T is undecidable. This contrasts with the situation for finite Church-Rosser Thue systems that are monadic. In addition, some problems are presented that are decidable for finite monadic Church-Rosser Thue systems, but that are undecidable in general for finite non-monadic Church-Rosser Thue systems. Finally, it is shown how degrees of complexity can be encoded in finite non-monadic Church-Rosser Thue systems.

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