Abstract
The problems arising come from genetics have been expressed as mathematical problems about the monoid of traces; Yuri Matiyasevich has modified some of these problems and they have become a problem of decidability of machines which seem to be very weak. One can find an introduction to traces in Diekert and Rozenberg (The Book of Traces, World Scientific, Singapore, 1995), and a study of this specific problem in Matiyasevich (Quadrature 27 (1997) 23). This is the proof of the decidability of the halting problem for Matiyasevich deterministic machines.
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