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

This is the published version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical Computer Science, 341, 1–3, (2005) DOI: 10.1016/j.tcs.2005.05.002This paper proves the decidability of several problems in the theory of HD 0L, D0L and PD 0L 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 HD 0L systems and the infinitude of PD 0L languages. Then, we prove the decidability of the problem of momentary stagnation of the growth function of PD 0L 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 HD 0L as a trivial consequence.This paper has been partially sponsored by the UPV/EHU project number 9/upv 00003.230-13707/2001. This paper has been partially sponsored by the Spanish Ministry of Science and Technology (MCYT) project number TIC2002-01948