On the enumerating series of an abstract numeration system

2011/08/29 by Pierre-Yves Angrand, Angrand, Pierre-Yves, Jacques Sakarovitch +1
Computer Science · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #cs.DM #cs.FL

paper · pdf · doi:10.48550/arxiv.1108.5711

presented at the Journées Montoises d'Informatique Théorique 2010, Sept. 2010, Amiens (France)

arxiv created 2011/08/29 · arxiv updated 2011/08/30

Abstract

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 numbers. It is also shown that conversely it is decidable whether an N-rational series corresponds to a rational abstract numeration system.

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