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A General Framework for Sequential Grammars with Control Mechanisms

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Descriptional Complexity of Formal Systems (DCFS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11612))

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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.

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Acknowledgements

I am very grateful to my colleagues and co-authors for many fruitful discussions as well as for their contributions to the topics described in this overview paper: First parts for the concept of the general framework were already discussed and elaborated during my stay in Magdeburg with Jürgen Dassow nearly thirty years ago. Afterwards, partial results were used in several papers, for example, with Henning Fernau, Markus Holzer, and Gheorghe Păun. The first comprehensive collection of results in [13] then was elaborated with my colleagues in Vienna, Marion Oswald and Marian Kogler. Recent results, especially for sequential grammars with activation and blocking of rules (see [2, 3]), were elaborated together with Artiom Alhazov and Sergiu Ivanov.

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Authors and Affiliations

  1. Faculty of Informatics, TU Wien, Favoritenstraße 9-11, 1040, Vienna, Austria

    Rudolf Freund

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  1. Rudolf Freund
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Correspondence to Rudolf Freund .

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Editors and Affiliations

  1. Slovak Academy of Sciences, Košice, Slovakia

    Michal Hospodár

  2. Slovak Academy of Sciences, Košice, Slovakia

    Galina Jirásková

  3. Saint Mary's University, Halifax, NS, Canada

    Stavros Konstantinidis

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Freund, R. (2019). A General Framework for Sequential Grammars with Control Mechanisms. In: Hospodár, M., Jirásková, G., Konstantinidis, S. (eds) Descriptional Complexity of Formal Systems. DCFS 2019. Lecture Notes in Computer Science(), vol 11612. Springer, Cham. https://doi.org/10.1007/978-3-030-23247-4_1

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  • DOI: https://doi.org/10.1007/978-3-030-23247-4_1

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  • Print ISBN: 978-3-030-23246-7

  • Online ISBN: 978-3-030-23247-4

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