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 (sDOL 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 sDOL system in polynomial time

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

A Method for Deciding the Finiteness of Synchronous, Tabled Picture Languages

In the present paper, synchronous, tabled chain code picture systems based on Lindenmayer systems (sT0L systems) are studied with respect to the finiteness of their picture languages. The finiteness is proved to be decidable. Additionally, a method is given for deciding whether an sT0L system generates a finite picture language or not. 1