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Bounds are given on the number of broken derived terms (a variant of Antimirov's 'partial derivatives') of a rational expression E. It is shown that this number is less than or equal to 2ℓ(E) + 1 in the general case, where ℓ(E) is the literal length of the expression E, and that the classical bound ℓ(E) + 1 which holds for partial derivatives also holds for… (More)

It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple computation of the value of words in this system and easy constructions for the recognition of recognisable sets of… (More)

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