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“…They found that addition machines form a natural model and they provided various algorithms for arithmetic on them, in particular as Floyd and Knuth looked for alternatives to the usual Turing machine models with their tiny primitive steps. Anisimov [1,2] studied the idea of Floyd and Knuth of using ideas borrowed from Fibonacci numbers for implementing arithmetic on large numbers with addition and investigated it thoroughly; later, he and Novokshonov [3,4,23] implemented the algorithms of Floyd and Knuth [3,4,23]. Schönhage [26] has proven that allowing subtraction and comparison increases the power of machines which can only add and do equality iff allowing division increases the power of such machines.…”

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“…They found that addition machines form a natural model and they provided various algorithms for arithmetic on them, in particular as Floyd and Knuth looked for alternatives to the usual Turing machine models with their tiny primitive steps. Anisimov [1,2] studied the idea of Floyd and Knuth of using ideas borrowed from Fibonacci numbers for implementing arithmetic on large numbers with addition and investigated it thoroughly; later, he and Novokshonov [3,4,23] implemented the algorithms of Floyd and Knuth [3,4,23]. Schönhage [26] has proven that allowing subtraction and comparison increases the power of machines which can only add and do equality iff allowing division increases the power of such machines.…”