## Circular Contextual Insertions/Deletions with Applications to Biomolecular Computation (1999)

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Citations: | 8 - 0 self |

### BibTeX

@MISC{Daley99circularcontextual,

author = {Mark Daley and Lila Kari and Greg Gloor and Rani Siromoney},

title = {Circular Contextual Insertions/Deletions with Applications to Biomolecular Computation},

year = {1999}

}

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### Abstract

Insertions and deletions of small circular DNA strands into long linear DNA strands are phenomena that happen frequently in nature and thus constitute an attractive paradigm for biomolecular computing. This paper presents a new model for DNA-based computation that involves circular as well as linear molecules, and that uses the operations of insertion and deletion. After introducing the formal model we investigate its properties and prove in particular that the circular insertion/deletion systems are capable of universal computation. We also give the results of an experimental laboratory implementation of our model. This shows that rewriting systems of the circular insertion/deletion type are viable alternatives in DNA computation. 1 Introduction Early models of DNA recombination, the splicing systems, have already been defined by [4]. They aimed to describe the action of restriction enzymes and ligases on DNA molecules which resulted in cleavage and reassociation of DNA strands. Almo...

### Citations

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Citation Context ... already been defined by [4]. They aimed to describe the action of restriction enzymes and ligases on DNA molecules which resulted in cleavage and reassociation of DNA strands. Almost a decade later, =-=[1]-=- reported the first experiment that practically used DNA molecules for computation. The experiment consisted in finding a laboratory solution of an instance of the Directed Hamiltonian Path Problem so... |

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Citation Context ...ences of letters in v, counting repetitions. For a language L, by L we denote the set of all words v where v 2 L. For further formal language definitions and notations the reader is referred to [12], =-=[13]-=-. 1 BA 2 3 x y x y 4 A x A Figure 1. Graphical representation of a circular insertion in the context (x; y), wherethe circular string is cut at the site (A; B). B By A x y B 2 Circular contextual guid... |

214 |
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Citation Context ...occurrences of letters in v, counting repetitions. For a language L, by L we denote the set of all words v where v 2 L. For further formal language definitions and notations the reader is referred to =-=[12]-=-, [13]. 1 BA 2 3 x y x y 4 A x A Figure 1. Graphical representation of a circular insertion in the context (x; y), wherethe circular string is cut at the site (A; B). B By A x y B 2 Circular contextua... |

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Citation Context ...riting systems of the circular insertion/deletion type are viable alternatives in DNA computation. 1 Introduction Early models of DNA recombination, the splicing systems, have already been defined by =-=[4]-=-. They aimed to describe the action of restriction enzymes and ligases on DNA molecules which resulted in cleavage and reassociation of DNA strands. Almost a decade later, [1] reported the first exper... |

59 |
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Citation Context ...n formal language theory, the operations of insertion and deletion have recently become of interest in connection with the topic of biomolecular computing. The insertion operation has been studied in =-=[7]-=- as a generalization of catenation. Given words u and v, the insertion of v into u consists of all words that can be obtained by inserting v in an arbitrary position of u: u , v = fu1vu2j u = u1u2;u1;... |

33 | DNA computing: arrival of biological mathematics
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Citation Context ...uncil of Canada. Since then, research in DNA computing has embraced both theoretical studies of models of DNA computation and experiments giving DNA solutions to mathematical problems, [3], [5], [6], =-=[8]-=-. In particular, [9] proposed a model of DNA computation based on insertions and deletions that could be implemented in the laboratory by using a technique called PCR site-specific oligonucleotide mut... |

22 | On the power of circular splicing systems and DNA computability
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(Show Context)
Citation Context ...sertions and deletions of words that aims to model these processes. (Note that circular DNA strings have been studied in the literature in the context of the splicing system model in [5], [11], [14], =-=[15]-=-.) Given a pair (x; y) of words called a context and a pair of words ( ; ) called a guide, thecircular contextual guided insertion of the circular string v into the linear string u is performed as fol... |

17 | Contextual insertions/deletions and computability
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Citation Context ...ce then, research in DNA computing has embraced both theoretical studies of models of DNA computation and experiments giving DNA solutions to mathematical problems, [3], [5], [6], [8]. In particular, =-=[9]-=- proposed a model of DNA computation based on insertions and deletions that could be implemented in the laboratory by using a technique called PCR site-specific oligonucleotide mutagenesis. Insertions... |

16 |
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Citation Context ...esearch Council of Canada. Since then, research in DNA computing has embraced both theoretical studies of models of DNA computation and experiments giving DNA solutions to mathematical problems, [3], =-=[5]-=-, [6], [8]. In particular, [9] proposed a model of DNA computation based on insertions and deletions that could be implemented in the laboratory by using a technique called PCR site-specific oligonucl... |

14 |
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Citation Context ...ch Council of Canada. Since then, research in DNA computing has embraced both theoretical studies of models of DNA computation and experiments giving DNA solutions to mathematical problems, [3], [5], =-=[6]-=-, [8]. In particular, [9] proposed a model of DNA computation based on insertions and deletions that could be implemented in the laboratory by using a technique called PCR site-specific oligonucleotid... |

13 |
and circular splicing systems
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(Show Context)
Citation Context ...zation of insertions and deletions of words that aims to model these processes. (Note that circular DNA strings have been studied in the literature in the context of the splicing system model in [5], =-=[11]-=-, [14], [15].) Given a pair (x; y) of words called a context and a pair of words ( ; ) called a guide, thecircular contextual guided insertion of the circular string v into the linear string u is perf... |

4 |
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(Show Context)
Citation Context ... of insertions and deletions of words that aims to model these processes. (Note that circular DNA strings have been studied in the literature in the context of the splicing system model in [5], [11], =-=[14]-=-, [15].) Given a pair (x; y) of words called a context and a pair of words ( ; ) called a guide, thecircular contextual guided insertion of the circular string v into the linear string u is performed ... |

3 | Contextual insertions/ deletions and computability - Kari - 1996 |

1 |
Closure properties of certain families of formal languages with respect to a generalization of cyclic closure
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(Show Context)
Citation Context ...thus to show that it is closed under cyclic permutation (the first phase), and also under linear insertion (the second phase). As it is known that REG,CF,CS and RE are closed under cyclic permutation =-=[2]-=-, and under ordinary insertion [7], it follows that they are closed also under circular insertion (C = G = f ; g). As REG, CF, CS, RE are all closed under contextual insertion [9] and circular permuta... |

1 | Formal models of DNA computation
- Daley, Eramian
- 1998
(Show Context)
Citation Context ...ringResearch Council of Canada. Since then, research in DNA computing has embraced both theoretical studies of models of DNA computation and experiments giving DNA solutions to mathematical problems, =-=[3]-=-, [5], [6], [8]. In particular, [9] proposed a model of DNA computation based on insertions and deletions that could be implemented in the laboratory by using a technique called PCR site-specific olig... |