Towards a proof of the decidability of the momentary stagnation of the growth function of D0L systems

This paper proves the decidability of several problems in the theory of HD0L, D0L and PD0L systems, some of which that have been proved before but are now proved in a different way. First, the paper tackles the decidability of the nilpotency of HD0L systems and the infinitude of PD0L languages. Then, we prove the decidability of the problem of momentary stagnation of the growth function of PD0L systems. Finally, we suggest a way to solve the decidability of the momentary stagnation of the growth function of D0L systems, proving the decidability of the infinitude of HD0L as a trivial consequence.