A DNA computing inspired computational model

In this paper we propose a universal rewriting system whose computational steps closely resemble the manner in which nature computes double stranded DNA molecules. The basic data structure is given by a couple of strings paired by a complementarity relation (such as the Watson-Crick one), and the rewriting rules have a biotechnological implementation as DNA computing standard procedures. The antiparallel orientation of the formal strings laying on the double structure is taken into consideration, as in [G. Franco, V. Manca, An algorithmic analysis of DNA structure, Soft Computing-A Fusion of Foundations, Methodologies and Applications 9 (10) (2005) 761-768] it was shown to be essential for some informational and computational aspects underlying the DNA autoduplication process. The universality of such a system has been proved and the biotechnological details of a possible implementation have been outlined. Moreover, the membrane system which turned out to be the natural context to describe our system in [G. Franco, M. Margenstern, Computing by Floating Strings, in: N. Busi, C. Zandron (Eds.), Proceedings of the First Workshop on Membrane Computing and Biologically Inspired Process Calculi (MeCBIC 2006), July 9, S. Servolo, Venice, Italy, in: ENTCS, vol. 171(issue 2), July 2007, pp. 95-104] has been proposed here in more technical detail, and the announced extension work has been developed.

[1]  E. Shapiro,et al.  Programmable and autonomous computing machine made of biomolecules , 2001, Nature.

[2]  Maurice Margenstern,et al.  On quasi-unilateral universal Turing machines , 2001, Theor. Comput. Sci..

[3]  Vincenzo Manca.  On the Logic and Geometry of Bilinear Forms , 2005, Fundam. Informaticae.

[4]  Takashi Yokomori,et al.  Linearizer and Doubler : Two Mappings to Unify Molecular Computing Models Based on DNA Complementarity , 2005, DNA.

[5]  Paul W. K. Rothemund,et al.  A DNA and restriction enzyme implementation of Turing machines , 1995, DNA Based Computers.

[6]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[7]  Giuditta Franco.  Biomolecular Computing – Combinatorial Algorithms and Laboratory Experiments (Doctoral Thesis) , 2006 .

[8]  Maurice Margenstern,et al.  On the Optimal Number of Instructions for Universal Turing Machines Connected With a Finite Automaton , 2003, Int. J. Algebra Comput..

[9]  Yurii Rogozhin,et al.  Small Universal Turing Machines , 1996, Theor. Comput. Sci..

[10]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

[11]  F. Young.  Biochemistry , 1955, The Indian Medical Gazette.

[12]  Vincenzo Manca,et al.  An algorithmic analysis of DNA structure , 2005, Soft Comput..

[13]  Maurice Margenstern,et al.  Computing by Floating Strings , 2007, Electron. Notes Theor. Comput. Sci..

[14]  榊原 康文,et al.  G. Paun, G. Rozenberg and A. Salomaa : "DNA Computing-New Computing Paradigms", Springer-Verlag (1998) , 2000 .

[15]  Laura F. Landweber,et al.  Fully Controllable Microfluidics for Molecular Computers , 2004 .

[16]  David I. Lewin,et al.  DNA computing , 2002, Comput. Sci. Eng..

[17]  Ehud Shapiro,et al.  Bringing DNA computers to life , 2006 .

[18]  M. Margenstern,et al.  Deux machines de Turing universelles à au plus deux instructions gauches , 1995 .

[19]  M. Margenstern,et al.  Une machine de Turing universelle non-effaçante à exactement trois instructions gauches , 1995 .