Periodicity and ultimate periodicity of D0L systems

A new proof for the decidability of D0L ultimate periodicity

L systems were originally introduced by A. Lindenmayer to model the development of simple filamentous organisms [6, 7]. The challenging and fruitful study of these systems in the 70s and 80s created many new results and notions [9]. In this paper we consider the important problem of recognizing ultimately periodic D0L sequences. Let A be a finite alphabet and denote the empty word by ε . A D0L ...

Automata, Boolean Matrices, and Ultimate Periodicity

This paper presents a Boolean-matrix-based method to automata theory, with an application to the study of regularity-preserving functions. A new characterization of such functions is derived in terms of the property of ultimate periodicity with respect to powers of Boolean matrices. This characterization reveals the intrinsic algebraic nature of regularity-preserving functions. It facilitates a...

Decidability of the HD0L ultimate periodicity problem

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

Periodicity and Almost-periodicity

Periodicity and Quasi-periodicity for Super-integrable Hamiltonian Systems

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single-valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a com-mensurability condition is imposed on an angular momentum component. R ´ ESUMÉ...