Linear numeration systems of order two (Q1105378)

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.