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… 
At the Crossroads of Linguistics , DNA Computing , and Formal Language Theory : Characterizing RE Using Insertion-Deletion Systems 1
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
  • F. BashaSindhu J. Kumaar
  • Computer Science
    2016 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC)
  • 2016
TLDR
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.
...
...

References

SHOWING 1-10 OF 26 REFERENCES
Deletion operations: closure properties
TLDR
Some variants of deletion operations which generalize the left/right quotient of languages are studied, and how these deletions can be expressed as a combination of other operations, and on closure properties of various language families under deletion are studied.
On Language Equations with Invertible Operations
  • L. Kari
  • Mathematics
    Theor. Comput. Sci.
  • 1994
A DNA and restriction enzyme implementation of Turing machines
TLDR
An encoding for the transition table of a Turing machine in DNA oligon nucleotides and a corresponding series of restrictions and ligations that simulate the operation of the Turing machine encoded in those oligonucleotides are proposed.
DNA computers in vitro and vivo
| We show how DNA molecules and standard lab techniques may be used to create a nonde-terministic Turing machine. This is the rst scheme that shows how to make a universal computer with DNA. We claim
Two theorems about Galiukschov semicontextual languages
  • G. Paun
  • Computer Science, Mathematics
    Kybernetika
  • 1985
Resolution d'un probleme ouvert (il y a des grammaires semi-contextuelles de degre 2 qui generent des langages non CF) et extension d'un resultat, concernant les proprietes de fermeture des familles
Formal languages I
TLDR
Find the secret to improve the quality of life by reading this formal languages by knowing who the author is, how well-known the work is, and so on.
Molecular computation of solutions to combinatorial problems.
TLDR
This experiment demonstrates the feasibility of carrying out computations at the molecular level by solving an instance of the directed Hamiltonian path problem with standard protocols and enzymes.
A Laboratory manual
``On Insertions and Deletions in Formal Languages,'
  • Ph.D. thesis,
  • 1991
...
...