Abstract
We describe a formal language/notation for DNA molecules that may contain nicks and gaps. The elements of the language, DNA expressions, denote formal DNA molecules. Different DNA expressions may denote the same formal DNA molecule. We analyse the shortest DNA expressions denoting a given formal DNA molecule. We determine lower bounds on their lengths and explain how we construct these minimal DNA expressions.
Similar content being viewed by others
References
LM Adleman (1994) ArticleTitleMolecular computation of solutions to combinatorial problems Science 266 1021–1024
D Boneh C Dunworth RJ Lipton (1996) Breaking DES using a molecular computer RJ Lipton EB Baum (Eds) DNA Based Computers, Proceedings of a DIMACS workshop, April 4, 1995 Princeton University, American Mathematical Society Providence, RI 37–66
J Chen J Reif (Eds) (2004) DNA Computing, 9th International workshop on DNA based computers, DNA9, Madison, WI, USA, June 1–3, 2003, Revised Papers, LNCS 2943 Springer-Verlag Berlin
C Ferretti G Mauri C Zandron (Eds) (2005) DNA Computing, 10th International workshop on DNA computing, DNA10, Milan, Italy, June 7–10, 2004, Revised Selected Papers, LNCS 3384 Springer-Verlag Berlin
T Head (1987) ArticleTitleFormal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors Bulletin of Mathematical Biology 49 IssueID6 737–759 Occurrence Handle0655.92008 Occurrence Handle923454 Occurrence Handle10.1016/S0092-8240(87)90018-8
Li Z (1999) Algebraic properties of DNA operations. In: Kari L, Rubin H and Wood DH (eds) Proceedings of the fourth international meeting on DNA based computers, University of Pennsylvania, Philadelphia, USA, June 15–19, 1998, BioSystems 52: 55–61
Gh Păun G Rozenberg A Salomaa (1998) DNA Computing – New Computing Paradigms Springer-Verlag Berlin
E Rivas SR Eddy (2000) ArticleTitleThe language of RNA: a formal grammar that includes pseudoknots Bioinformatics 16 IssueID4 334–340 Occurrence Handle10.1093/bioinformatics/16.4.334
van Vliet R (2004) Combinatorial aspects of minimal DNA expressions (ext.). Technical Report 2004–03, Leiden Institute of Advanced Computer Science, Leiden University, see www.liacs.nl/home/rvvliet/mindnaexpr.html
van Vliet R, Hoogeboom HJ and Rozenberg G (2005) Combinatorial aspects of minimal DNA expressions. In: Ferretti C, Mauri G, Zandron C (eds) DNA Computing, 10th International workshop on DNA computing, DNA10, Milan, Italy, June 7-10, 2004, Revised Selected Papers, LNCS 3384. Springer-Verlag, Berlin, pp. 375–388
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Van Vliet, R., Hoogeboom, H.J. & Rozenberg, G. The Construction of Minimal DNA Expressions. Nat Comput 5, 127–149 (2006). https://doi.org/10.1007/s11047-005-4464-y
Issue Date:
DOI: https://doi.org/10.1007/s11047-005-4464-y