Graph-Controlled Insertion-Deletion Systems

@inproceedings{Freund2010GraphControlledIS,
  title={Graph-Controlled Insertion-Deletion Systems},
  author={Rudolf Freund and Marian Kogler and Yurii Rogozhin and Sergey Verlan},
  booktitle={Workshop on Descriptional Complexity of Formal Systems},
  year={2010}
}
In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph: computational completeness can be obtained by systems with insertion or deletion rules involving at most two symbols in a contextual or in a context-free manner and with the control graph having only four nodes. 

Sequential and graph controlled insertion-deletion systems

  • F. BashaSindhu J. Kumaar
  • Computer Science
    2016 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC)
  • 2016
It is found that sequential operation in contextual system characterizes non synchronized pure pattern language (NSPPL) and context free language (CFL), and a variant in the insertion-deletion system called graph controlled contextual insertion- deletion also enables to generate non synchronizedpure pattern language which helps to improve the computational complexity.

Computational Completeness of Path-Structured Graph-Controlled Insertion-Deletion Systems

This work investigates which combinations of size parameters are sufficient to maintain the computational completeness of such restricted systems with the additional restriction that the control graph is a path, thus, these results also hold for ins-del P systems.

Matrix insertion-deletion systems

Universality of Graph-controlled Leftist Insertion-deletion Systems with Two States

This article introduces extended rules, in which the contexts may be specified as regular expressions, instead of fixed words, and proves that leftist systems with such extended rules and two-state graph control can simulate any arbitrary 2-tag system.

Generative Power of Matrix Insertion-Deletion Systems with Context-Free Insertion or Deletion

This work shows for instance that matrix insertion-deletion systems with matrices of length two, insertion rules of type 1,i?ź1, i?Ż1 and context-free deletions are computationally complete and how to simulate Kleene stars of metalinear languages with several types of systems with very limited resources.

On describing the regular closure of the linear languages with graph-controlled insertion-deletion systems

It is shown that whenever GCID systems (with certain syntactical restrictions) describe all linear languages (LIN) with t components, they can extend this to GC ID systems with just one more component to describe, for instance, the concatenation of two languages from the language family that can be described as the Kleene closure of linear languages.

Graph-Controlled Insertion-Deletion Systems Generating Language Classes Beyond Linearity

It is shown that whenever GCID systems describe \(\mathrm {LIN}\) with t components, this can be extended toGCID systems with just one more component to describe, for instance, 2-\(\Mathrm { LIN}\) and with further addition of one more components, the rational closure of \(\mathRM {LIN}\).

Random Context and Semi-conditional Insertion-deletion Systems

It is shown that conditional application of insertion and deletion rules strictly increases the computational power, and context-free insertion and delete rules of one symbol are sufficient to achieve computational completeness in the case of semi-conditional insertion-deletion systems.

P Systems with Insertion and Deletion Exo-Operations

This paper considers insertion-deletion P systems with insertion and deletion operations applied only at the ends of string, and shows that such systems with one-symbol insertion and delete of up to two symbols are computationally complete, and so are systems with inserted symbols and deleted symbols.

References

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    6th International Symposium on String Processing and Information Retrieval. 5th International Workshop on Groupware (Cat. No.PR00268)
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A new model for DNA-based computation that involves circular as well as linear molecules, and that uses the operations of insertion and deletion, is presented and it is proved that the circular insertion/deletion systems are capable of universal computation.