Abstract
The problem of decidability of the first order theory of one-step rewriting was stated in [CCD93]. One can find the problem on the lists of open problems in rewriting in [DJK93] and [DJK95]. In 1995 Ralf Treinen proved that the theory is undecidable.
In this paper we show that the theorem of Treinen is an easy consequence of a powerful tool first used to establish undecidability results in the theory of logic programming [MP92]. Then we use the tool to give strong refinements of the result of Treinen:
We show that (the ∃*∀* part of) the first order theory of one-step rewriting is undecidable for linear Noetherian rewriting systems.
Then we prove, what we consider to be quite a striking result, that (the ∃*∀*part of) the first order theory of one-step rewriting is undecidable even if the rewriting system is Noetherian and right-ground. Up to our knowledge it is the first known undecidable property of right-ground systems.
Partially supported by Polish KBN grant 3 P301 046 07
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© 1997 Springer-Verlag Berlin Heidelberg
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Marcinkowski, J. (1997). Undecidability of the first order theory of one-step right ground rewriting. In: Comon, H. (eds) Rewriting Techniques and Applications. RTA 1997. Lecture Notes in Computer Science, vol 1232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62950-5_75
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DOI: https://doi.org/10.1007/3-540-62950-5_75
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