On Controlling Rewriting by Properties of Strings and Symbols

In this paper we explore forms of organization of rewriting systems which allow the systematic modelling of systems for human-computer interaction and the control of their dynamics. To this end we exploit tools from formal languages, adopting forms of parallel rewriting from L-systems tradition. Based on this formalisation, a notion of controlled rewriting is proposed where information about how to rewrite strings is embedded into the strings themselves or in properties of symbols. The main contribution of the paper is the introduction of a variety of families of L-systems with new control mechanisms in their rewriting relations. Hierarchies in the families are discussed and some relations among them presented. We also start the exploration of the closure properties of these language families. Finally, we discuss some relations among the proposed families of L-systems and families of grammar systems.