# 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}
}
• Published in
Workshop on Descriptional…
7 August 2010
• Mathematics, Computer Science
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.
• 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.
• Mathematics, Computer Science
CIAA
• 2017
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.
• Computer Science, Mathematics
Theor. Comput. Sci.
• 2012
• Computer Science
MCU
• 2015
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.
• Computer Science
UCNC
• 2016
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.
• Computer Science
RAIRO Theor. Informatics Appl.
• 2018
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.
• Computer Science, Mathematics
DCFS
• 2017
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 $$\mathRM {LIN}$$.
• Computer Science
Fundam. Informaticae
• 2015
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.
• Computer Science
Fundam. Informaticae
• 2011
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

SHOWING 1-10 OF 24 REFERENCES

It is shown that if the length of the inserted/deleted string is bounded to two, then the obtained systems are not universal and a new complexity measure is introduced for insertion-deletion systems, which permits a better explanation of the obtained results.
• Mathematics, Computer Science
LATA
• 2008
The remaining open problem concerning the generative power of insertion-deletion systems having both contexts is solved by proving the computational completeness of systems having a context-free insertion of two symbols and a contextual deletion of one symbol.
• Computer Science, Mathematics
CSP
• 2008
This article takes two insertion-deletion systems that are not computationally complete, considers them in the framework of P systems and shows that the computational power is strictly increased by proving that any recursively enumerable language can be generated.
• Biology
• 1998
This chapter considers computing models based on two operations — insertion and deletion, with context dependence, which were already considered in formal language theory, mainly with motivation from linguistics.
• Computer Science
Natural Computing
• 2010
If context-free insertion and deletion rules of two symbols are used in combination with P systems, then the obtained model is still not computationally complete, but if the insertion and the deletion operations having same size are considered in the distributed framework of P systems then the computational power strictly increases and the obtained models become Computationally complete.
• Computer Science
MCU
• 2007
It is shown that a minimal deletion (of one symbol) in one-symbol one-sided context is sufficient for the computational completeness if a cooperation of 4 symbols is used for insertion rules and not sufficient if an insertion of one symbol in onesymbol left and right context is used.
The operations of insertion ((<---)) and iterated insertion ((<---)*) are simple variants of Kleene's operations (.) and (,*) ({Kle 56}) in a manner similar to the operations shuffle and iterated
• Computer Science, Biology
Natural Computing
• 2004
The generative power of insertion-deletion systems (InsDel systems) is investigated, and it is shown that the family INS11DEL11 is equal to the family of recursively enumerable languages.
• Biology, Computer Science
6th International Symposium on String Processing and Information Retrieval. 5th International Workshop on Groupware (Cat. No.PR00268)
• 1999
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.