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Linear numeration systems of order two. (English) Zbl 0648.68066
The author considers a numeration system $$(U_ v,s)$$ of the form $u_{n+2}=au_{n+1}+bu_ n,\quad u_ 0=1,\quad u_ 1=v\geq 2\quad.$ He shows that the system is complete only if $$v=a+1$$ and $$s=a$$. For the system $$(U_{a+1},a)$$ there exists a uniquely defined normal form of a word which may be computed by a composition of two subsequential machines. Addition of integers represented in $$(U_{a+1},a)$$ may be computed by a left-subsequential machine.
Reviewer: M.Frumkin

##### MSC:
 68Q45 Formal languages and automata 11B37 Recurrences 11A63 Radix representation; digital problems
##### Keywords:
numeration system; subsequential machines
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##### References:
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