Control Mechanisms for Array Grammars on Cayley Grids

A General Framework for Sequential Grammars with Control Mechanisms

“…For the basic notions and results of formal language theory the reader is referred to the monographs and handbooks in this area as [7], [23], and [24], and for the basics of group theory and group presentations to [15]. The definitions and examples given in the following subsection are the basis for developing the theory of array grammars defined on Cayley grids of finitely presented groups in Section 7 (see [10]).…”

“…We now recall the definition of sequential grammars with activation and blocking of rules in a similar way as introduced in [10,3,2].…”

“…Using a general model for graph-controlled, programmed, random-context, and ordered grammars of arbitrary type based on the applicability of rules, many relations between various regulating mechanisms for sequential grammars can be established in a very general setting without any reference to the underlying objects the rules are working on, as first exhibited in [12] in a comprehensive way. In this overview paper, the results elaborated in [12] are combined with the results obtained in the general framework for sequential grammars using activation and blocking of rules as introduced in [10], [3], and [2]. We recall special results for strings and multisets from [3] as well as results obtained in [10] for array grammars defined on Cayley grids of finitely presented groups.…”

“…In this overview paper, the results elaborated in [12] are combined with the results obtained in the general framework for sequential grammars using activation and blocking of rules as introduced in [10], [3], and [2]. We recall special results for strings and multisets from [3] as well as results obtained in [10] for array grammars defined on Cayley grids of finitely presented groups. Finally, we establish some even new general results for cooperating distributed grammar systems.…”

“…In the following section, we recall some notions from formal language and group theory, especially for Cayley grids of finitely presented groups. In Section 3 we recall the main definitions of the general framework for sequential grammars of arbitrary type and the control mechanisms based on the applicability of rules as initiated in [12] and then continued in [10] and [3], i.e., for graph-controlled, programmed, random-context, and ordered grammars, for grammars with a priority relation on the rules, as well as for sequential grammars with activation and blocking of rules.…”