# 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.Â

## 37 Citations

### Sequential and graph controlled insertion-deletion systems

- Computer Science2016 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

- Mathematics, Computer ScienceCIAA
- 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.

### On the computational completeness of graph-controlled insertion-deletion systems with binary sizes

- Computer ScienceTheor. Comput. Sci.
- 2017

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

- Computer ScienceMCU
- 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.

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

- Computer ScienceUCNC
- 2016

This work shows for instance that matrix insertion-deletion systems with matrices of length two, insertion rules of type 1,i?Åº1, i?Å»1 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

- Computer ScienceRAIRO 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.

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

- Computer Science, MathematicsDCFS
- 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 \(\mathRM {LIN}\).

### Random Context and Semi-conditional Insertion-deletion Systems

- Computer ScienceFundam. 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.

### P Systems with Insertion and Deletion Exo-Operations

- Computer ScienceFundam. 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

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- Computer ScienceDCFS
- 2005

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.

### Further Results on Insertion-Deletion Systems with One-Sided Contexts

- Mathematics, Computer ScienceLATA
- 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.

### Computational Power of P Systems with Small Size Insertion and Deletion Rules

- Computer Science, MathematicsCSP
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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.

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This chapter considers computing models based on two operations â€” insertion and deletion, with context dependence, which were already considered in formal language theory, mainly with motivation from linguistics.

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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.

### Insertion-Deletion Systems with One-Sided Contexts

- Computer ScienceMCU
- 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.

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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 iteratedâ€¦

### On the computational power of insertion-deletion systems

- Computer Science, BiologyNatural 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.

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- Biology, Computer Science6th 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.