## Simulation of Turing machines by a regular rewrite rule.(English)Zbl 0753.68052

Summary: We prove that for any Turing machine, there exists a regular (i.e. left- linear and nonoverlapping, also called orthogonal) and variable- preserving rule that simulates its behaviour. The main corollary is the undecidability of termination for such a rule.

### MSC:

 68Q42 Grammars and rewriting systems 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 03D03 Thue and Post systems, etc. 03D35 Undecidability and degrees of sets of sentences

### Keywords:

infinite rewriting; undecidability; termination
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### References:

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