Regulated Array Grammars of Finite Index. Part I: Theoretical Investigations

We consider regulated (n-dimensional) context-free array grammars of nite index, i.e., with a limited number of active areas. This research is motivated by the observation that in several practical applications of array grammars only such a bounded number of active areas is observed. Combined with diierent methods known from regulated rewriting (e.g., matrix grammars, programmed grammars, grammars with prescribed teams), this natural restriction to a limited number of non-terminal symbols occurring in the arrays during a derivation gives rise to various diierent families of array languages (depending on the type of context-free array productions used in the regulated array grammars working with various types of the nite index restriction). Moreover , in the second part we shall present a characterization of some of these families deened by regulated context-free array grammars working with a nite index restriction via special k-head nite array automata, which can be used in the eld of character recognition.