Abstract
We prove in this paper that for every Turing machine there exists a left-linear, variable preserving and non-overlapping rewrite rule that simulates its behaviour. The main corollary is the undecidability of the termination for such a rule. If we suppose that the left-hand side can be unified with an only subterm of the right-hand side, then termination is decidable.
Supported in part by the "GRECO de Programmation" and the PRC "Mathématiques et Informatique". Part of the ESPRIT Basic Research Actions, BRA "Algebraic and Syntactic Methods in Computer Science" and BRA "Computing by, Graph Transformations".
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© 1989 Springer-Verlag Berlin Heidelberg
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Dauchet, M. (1989). Simulation of Turing machines by a left-linear rewrite rule. In: Dershowitz, N. (eds) Rewriting Techniques and Applications. RTA 1989. Lecture Notes in Computer Science, vol 355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51081-8_103
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DOI: https://doi.org/10.1007/3-540-51081-8_103
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