On images of D0L and DT0L power series

AbstractThe D0L and DT0L power series are generalizations of D0L and DT0L languages. We continue the study of these series by investigating various decidability questions concerning the images of D0L and DT0L power series

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

Decidability of the HD0L ultimate periodicity problem

In this paper we prove the decidability of the HD0L ultimate periodicity problem

On the complete simulation of DOL schemes and locally catenative schemes

Let (Σ, h) be a DOL scheme where h is a homomorphism from Σ* to Σ*. (Σ, h) is said to completely simulate another DOL scheme (Δ, g) if hf = fg and hn = fr} for some injective homomorphism f, some positive integer n, and some homomorphism r. The main results of this paper are: (1) Each complete simulation can be decomposed into a series of “primitive” simulations. (2) It is decidable whether or not there exists a standard locally catenative scheme which is simulated by a given DOL scheme

Bispecial factors in circular non-pushy D0L languages

We study bispecial factors in fixed points of morphisms. In particular, we propose a simple method of how to find all bispecial words of non-pushy circular D0L-systems. This method can be formulated as an algorithm. Moreover, we prove that non-pushy circular D0L-systems are exactly those with finite critical exponent.Comment: 18 pages, 5 figure