Using Alternating Words to Describe Symbolic Pictures

In this paper we present the concepts of drawn symbolic picture and symbolic picture. Such notions have been conceived as an extension of the concept of drawn pictures which was introduced by Maurer, Rozenberg and Welzl [31]. We provide a string description of such pictures. It consists of alternating words, i.e. strings whose letters are in alternation from an alphabet of symbols and an alphabet of moves. We analyze the complexity of the description language of a (drawn) symbolic picture and show how these yield context-sensitive, contextfree and regular languages. Then, we characterize the grammars for alternating words and define the generative model for (drawn) symbolic pictures. Moreover, we investigate the different types of ambiguity that occur when dealing with symbolic grammars. Finally, we propose a classification for symbolic picture grammars and languages.