Abstract
Since more than five decades, many control mechanisms have been introduced for sequential string grammars, including control graphs, matrices, permitting and forbidden contexts, and order relations. These control mechanisms then have been extended to sequential grammars working on objects different from strings, for example, to array, graph, and multiset grammars. Many relations between the languages generated by sequential grammars working on these objects with different control mechanisms were shown to be similar to the relations already proved for the string case. Within a general framework for regulated rewriting based on the applicability of rules in sequential grammars, many relations between various control mechanisms can be established in a very general setting without any reference to the underlying objects the rules are working on. Besides the well-known control mechanisms as control graphs, matrices, permitting and forbidden rules, partial order on rules, and priority relations on rules, the new variants of activation of rules as well as activation and blocking of rules are considered. Special results for strings and multisets as well as for arrays in the general variant defined on Cayley grids of finitely presented groups are exhibited based on the general results. Finally, some general results for cooperating distributed grammar systems are established.
Highlights
Already thirty years ago, a first comprehensive overview on many concepts of regulated rewriting, especially for the string case, was given the monograph on regulated rewriting by Jurgen Dassow and Gheorghe Paun [7]
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
Most of the relations indicated by vectors even hold for arbitrary types X; needed features of being a strictly extended type or being a type with unit and/or trap rules are indicated by se, u, and t, respectively, aside the vector: L(X -GCac )
Summary
A General Framework for Sequential Grammars with Control Mechanisms. 21th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2019, KoĆĄice, Slovakia. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. Lâarchive ouverte pluridisciplinaire HAL, est destinĂ©e au dĂ©pĂŽt et Ă la diffusion de documents scientifiques de niveau recherche, publiĂ©s ou non, Ă©manant des Ă©tablissements dâenseignement et de recherche français ou Ă©trangers, des laboratoires publics ou privĂ©s
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