Addition machines, automatic functions and open problems of Floyd and Knuth

Floyd and Knuth investigated in 1990 register machines which can add, subtract compare integers as primitive operations. They asked whether their current bound on the number of registers for multiplying dividing fast (running time linear size input) be improved one output powers two summing up to a positive integer subquadratic time. Both questions are answered positively. Furthermore, it is shown that every function computed by only automatic functions with input four time; larger inputs 5 There nonautomatic