## DNA Computing, Matching Systems, and Universality (1996)

Citations: | 2 - 1 self |

### BibTeX

@TECHREPORT{Kari96dnacomputing,,

author = {Lila Kari and Gheorghe Paun and Grzegorz Rozenberg and Arto Salomaa and Sheng Yu},

title = {DNA Computing, Matching Systems, and Universality},

institution = {},

year = {1996}

}

### OpenURL

### Abstract

We introduce the matching systems, a computability model which is an abstraction of the way of using the Watson-Crick complementarity when computing with DNA in the Adleman style, [1]. Several types of matching systems are shown to have the same power as finite automata, one variant is proven to be equivalent to Turing machines, and another one is found to have a strictly intermediate power. TUCS Research Group Mathematical Structures of Computer Science 1. Introduction The matching systems introduced here are language generating devices based on the matching operation, which, in turn, is a model of the techniques used by L. Adleman in his successful experiment of computing a Hamiltonian path in a graph by using DNA, [1]. We recall some details of the experiment in order to see the roots of our models. One knows that DNA sequences are in fact double stranded (helicoidal) structures composed of four nucleotides, A (adenine), C (cytosine), G (guanine) , and T (thymine), paired A--T, ...

### Citations

612 | Molecular computation of solution to combinatorial problems
- Adleman
- 1994
(Show Context)
Citation Context ... 1239-1891 Abstract We introduce the matching systems, a computability model which is an abstraction of the way of using the Watson-Crick complementarity when computing with DNA in the Adleman style, =-=[1]-=-. Several types of matching systems are shown to have the same power as finite automata, one variant is proven to be equivalent to Turing machines, and another one is found to have a strictly intermed... |

487 | Regular Languages - Yu |

188 |
Formal Language Theory and DNA: An Analysis of the Generative Capacity of Specific Recombinant Behaviors
- Head
- 1987
(Show Context)
Citation Context ...s obtained in a series of papers (see references in [10], [13], [16]) about the possibility of designing universal (and programmable) DNA "computers" based on the operation of splicing, intr=-=oduced in [9]-=- as a model of the recombinant behavior of DNA under the influence of 2 restriction enzymes and ligases. 3. The matching operation Take an alphabet V (a finite set of abstract symbols) endowed with a ... |

116 |
Regulated Rewriting in Formal Language Theory
- Păun
- 1989
(Show Context)
Citation Context ...! ) checks whether or not the number of symbols d and d 0 is the same. Now, clearly, L f (fl) = f(g \Gamma1 (L(G 0 ))). The family MAT is closed under arbitrary morphisms and under inverse morphisms (=-=[5]-=-), hence L f (fl) 2 MAT . 2 20 Open problem. Is the family FML included in CF (or in LIN) ? 7. Final remarks We have found characterizations of families REG and RE using variants of matching systems. ... |

59 | Speeding up computations via molecular biology - Lipton - 1996 |

49 | Petri nets algorithms in the theory of matrix grammars
- Hauschild, Jantzen
- 1994
(Show Context)
Citation Context ...esis we have FML ` RE. For the strictness, we shall prove that FML ` MAT , where MAT is the family of languages generated by context-free matrix grammars with arbitrary rules. Because MAT ae RE ([6], =-=[8]-=-), we obtain FML ae RE. Consider a matching system fl = (V; ae; T; f; g; A; B d ; B u ). Define V 0 = fa 0 j a 2 V g; L(A) = f[a 1 ; b 0 1 ] : : : [a k ; b 0 k ]a k+1 : : : a k+r j k; rs0; k + rs1; ` ... |

47 | Using DNA to solve NP-Complete Problems - Lipton - 1995 |

41 | Regular extended H systems are computationally universal - Paun - 1996 |

23 |
Language theory and molecular genetics. Generative mechanisms suggested by DNA recombination, chapter 7
- Păun
(Show Context)
Citation Context ...s" could be imagined just using the Watson-Crick complementarity, plus the techniques required in the mentioned restriction. This reminds the results obtained in a series of papers (see reference=-=s in [10], [13], [1-=-6]) about the possibility of designing universal (and programmable) DNA "computers" based on the operation of splicing, introduced in [9] as a model of the recombinant behavior of DNA under ... |

22 | DNA computing based on splicing: the existence of universal computers - Păun |

16 |
DNA computing based on the splicing operation
- Paun, Salomaa
- 1996
(Show Context)
Citation Context ...imagined just using the Watson-Crick complementarity, plus the techniques required in the mentioned restriction. This reminds the results obtained in a series of papers (see references in [10], [13], =-=[16]) about th-=-e possibility of designing universal (and programmable) DNA "computers" based on the operation of splicing, introduced in [9] as a model of the recombinant behavior of DNA under the influenc... |

14 |
Salomaa: Grammars with controlled derivations
- Păun
- 1997
(Show Context)
Citation Context ...ch thesis we have FML ` RE. For the strictness, we shall prove that FML ` MAT , where MAT is the family of languages generated by context-free matrix grammars with arbitrary rules. Because MAT ae RE (=-=[6]-=-, [8]), we obtain FML ae RE. Consider a matching system fl = (V; ae; T; f; g; A; B d ; B u ). Define V 0 = fa 0 j a 2 V g; L(A) = f[a 1 ; b 0 1 ] : : : [a k ; b 0 k ]a k+1 : : : a k+r j k; rs0; k + rs... |

12 | II: A purely homomorphic characterization of recursively enumerable sets - Culik - 1979 |

11 |
A challenge for formal language theorists
- Păun
- 1995
(Show Context)
Citation Context ...ld be imagined just using the Watson-Crick complementarity, plus the techniques required in the mentioned restriction. This reminds the results obtained in a series of papers (see references in [10], =-=[13], [16]) ab-=-out the possibility of designing universal (and programmable) DNA "computers" based on the operation of splicing, introduced in [9] as a model of the recombinant behavior of DNA under the in... |

10 | DNA Computing Based on Splicing: Universality Results - Păun - 2000 |

10 | Salomaa: Computing by splicing, Theor - Păun, A - 1996 |

8 | On constructing a molecular computer, Manuscript in circulation - Adleman - 1995 |

6 |
Equality sets for homomorphisms of free monoids, Acta Cybernetica 4
- Salomaa
- 1978
(Show Context)
Citation Context ...) is the equality set of h 1 and h 2 , and h T is a special projective morphism defined by h T (a) = ( a; if a 2 T ; ; if a 62 T: A representation which is very similar to the above has been shown in =-=[18], [19-=-]: L = h T (E(h 1 ; h 2 ) " R): (2) The difference between (1) and (2) is that (1) uses the h 1 image of the equality set of h 1 and h 2 , i.e., h 1 (E(h 1 ; h 2 )) (= h 2 (E(h 1 ; h 2 ))), but (... |

6 |
of Formal Language Theory, Computer Science
- Salomaa, Jewels
- 1981
(Show Context)
Citation Context ... and, the other, a specific construction with matching systems. The essence of our proof can be described as follows. The notion of coherence comes very close to the idea of the twinshuffle languages =-=[19]-=-. Hence, the generative capacity of the latter can be carried over to matching systems. We now begin the details. From the Turing-Church thesis we have the following lemma: Lemma 6. CML ` RE: 11 In vi... |