In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from - lower and upper bounds on growth rate; in particular boundedness, images, regularity (recognizability by deterministic finite automaton) preimages, factors, such as squares palindromes We show that the are undecidable.

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...