# Contextual Insertions/Deletions and Computability

@article{Kari1996ContextualIA, title={Contextual Insertions/Deletions and Computability}, author={Lila Kari and Gabriel Thierrin}, journal={Inf. Comput.}, year={1996}, volume={131}, pages={47-61} }

We investigate two generalizations of insertion and deletion of words, that have recently become of interest in the context of molecular computing. Given a pair of words (x, y), called a context, the (x, y)-contextual insertion of a wordvinto a worduis performed as follows. For each occurrence ofxyas a subword inu, we include in the result of the contextual insertion the words obtained by insertingvintou, betweenxandy. The (x, y)-contextual deletion operation is defined in a similar way. We…

## 130 Citations

At the Crossroads of Linguistics , DNA Computing , and Formal Language Theory : Characterizing RE Using Insertion-Deletion Systems 1

- Computer Science
- 2007

The results show that these operations, even with strong restrictions on the length of the contexts and/or on thelength or on the form of the inserted/deleted words are computationally complete, they can simulate the work of any Turing machine.

Transposition based contextual insertion on linear DNA strands with deletion precedence

- Computer ScienceInt. J. Comput. Math.
- 2004

In the proposed system, single contextual insertion and usual (with two contexts) contextual deletions are used and it is assumed that the deletion operation has higher precedence than insertions, if both are possible at a moment.

Single semi-contextual insertion-deletion systems

- Mathematics, Computer ScienceNat. Comput.
- 2021

If forbidding strings of size 2 and permitting strings ofsize 1 are used then computational completeness can be achieved and checking for a single permitting symbol is sufficient and it is shown that in the case of systems having rules with forbidding conditions only, all regular languages can be obtained.

Representations and Characterizations of Languages in Chomsky Hierarchy by Means of Insertion-Deletion Systems

- Computer Science, LinguisticsInt. J. Found. Comput. Sci.
- 2008

A new characterization of insertion-deletion operations in linguistics and in DNA computing is contributed with a new representation of this type, as well as with representations of regular and context-free languages, mainly starting from context- free insertion systems of as small as possible complexity.

Context Insertions

- MathematicsComputation, Cooperation, and Life
- 2011

It is proved that all the properties of a contextual scheme X, which provides a selection criterion for contextual insertion in a language L, are decidable for regular languages.

Circular Post Machines and P Systems with Exo-insertion and Deletion

- Computer ScienceInt. Conf. on Membrane Computing
- 2011

The main aim of this paper is to consider the operations applied at the ends of the string, and prove the computational completeness in case of priority of deletion over insertion, and introduce a new variant (CPM5) of circular Post machines: those with instructions changing a state and either reading one symbol or writing one symbol.

Restricted Insertion-Deletion Systems

- Computer Science
- 2004

This paper shows that the same generative capacity can be obtained even if the generated language of an insertion-deletion system is defined the traditional way, and that a two-letter alphabet is enough to generate any recursively enumerable language.

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.

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.

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