On the generating functions of languages accepted by deterministic one-reversal counter machines

We prove that the generating function of a language accepted by a one-way deterministic one-reversal counter machine without negative cycles is holonomic. The result is achieved by solving a particular case of the conjecture L _DFCM=RCM. Here, RCM is a class of languages that has been recently introduced and that admits some interesting properties , namely it contains only languages with holonomic generating function .