1. Origin and Motivation. 2. Formal Language Theory Prerequisites. 3. Contexts (Adjoining) Everywhere. 4. Basic Classes of Contextual Grammars. 5. Generative Capacity. 6. Language Theoretic Properties. 7. Linguistically Relevant Properties. 8. Grammars with Restricted Selection. 9. Grammars with Minimal/Maximal Use of Selectors. 10. Variants of Contextual Grammars. 11. Two-Level Contextual Grammars. 12. Regulated Contextual Grammars. 13. A Generalization: n-Contextual Grammars. 14. A Dual Model: Insertion Grammars. 15. Further Topics. 16. Open Problems and Research Topics. Bibliography. Subject Index.

This is a comprehensive (and friendly) introduction to membrane computing (MC), meant to offer both computer scientists and non-computer scientists an up-to-date overview of the field. That is why the set of notions introduced here is rather large, but the presentation is informal, without proofs and with rigorous definitions given only for the basic types of P systems — symbol object P systems with multiset rewriting rules, systems with symport/antiport rules, systems with string objects, tissue-like P systems, and neural-like P systems. Besides a list of (biologically inspired or mathematically motivated) ingredients/features which can be used in systems of these types, we also mention a series of results, as well as a series of research trends and topics.

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Marcus Contextual Grammars

Introduction to Membrane Computing

We consider a class of insertion-deletion systems which have not been investigated so far, those without any context controlling the insertion-deletion operations. Rather unexpectedly, we found that context-free insertion-deletion systems characterize the recursively enumerable languages. Moreover, this assertion is valid for systems with only one axiom, and also using inserted and deleted strings of a small length. As direct consequences of the main result we found that set-conditional insertion-deletion systems with two axioms generate any recursively enumerable language (this solves an open problem), as well as that membrane systems with one membrane having context-free insertion-deleletion rules without conditional use of them generate all recursively enumerable languages (this improves an earlier result). Some open problems are also formulated.

Context-free insertion-deletion systems

Contextual grammars were introduced by S. Marcus in 1969 [29], in an attempt to build a bridge between analytical and generative models of natural languages. In particular, contextual grammars were “translating” the central notion of context from the analytical models into the framework of generative grammars. The chapter by S. Marcus in this handbook [31] gives a lucid account of the motivation behind contextual grammars from the natural point of view.

Contextual grammars and formal languages

We investigate the class of context-free insertion-deletion systems. It is known that such systems are universal if the length of the inserted/deleted string is at least three. We show that if this length is bounded to two, then the obtained systems are not universal. We characterise the obtained class and we introduce a new complexity measure for insertion-deletion systems, which permits a better explanation of the obtained results.

/pdf/on-minimal-context-free-insertion-deletion-systems-1tpbwagnok.pdf

Marcus Contextual Grammars

Citations

Introduction to Membrane Computing

Context-free insertion-deletion systems

Contextual grammars and formal languages

On minimal context-free insertion-deletion systems

On Minimal Context-Free Insertion-Deletion Systems

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