On the Finiteness of Picture Languages of Synchronous Deterministic Chain Code Picture Systems

Chain Code Picture Systems are Lindenmayer systems over a special alphabet. The strings generated are interpreted as pictures. This leads to Chain Code Picture Languages. In this paper, synchronous deterministic Chain Code Picture Systems (sD0L systems) are studied with respect to the finiteness of their picture languages. First, a hierarchy of abstractions is developed, in which the interpretation of a string as a picture passes through a multilevel process. Second, on the basis of this hierarchy, an algorithm is designed which decides the finiteness or infiniteness of any sD0L system in polynomial time.