A Formal Notation for DNA

A Minimal Normal Form for DNA Expressions

The first paper is entitled
*Making DNA Expressions Minimal*.
The abstract of this paper reads:

*
DNA expressions constitute a formal notation
for DNA molecules that may contain nicks and gaps.
Different DNA expressions may denote the same DNA molecule.
We describe an algorithm to rewrite a given DNA expression
into a DNA expression
of minimal length denoting the same molecule.
*

The paper is available here (as pdf). You can also find the paper directly at the publisher's website, when you follow this link.

The second paper is entitled
*A Minimal Normal Form for DNA Expressions*.
The abstract of this paper reads:

*
DNA expressions constitute a formal notation
for DNA molecules that may contain nicks and gaps.
Different DNA expressions may denote the same DNA molecule.
We define a (minimal) normal form for the language of DNA expressions,
and describe an algorithm to rewrite a given DNA expression
into the normal form.
*

The paper is available here (as pdf). You can also find the paper directly at the publisher's website, when you follow this link.

You may refer to the papers as

R. van Vliet, H.J. Hoogeboom:
Making DNA expressions minimal,
*Fundamenta Informaticae*,
**123**(2), 2013, 199-226

and R. van Vliet, H.J. Hoogeboom:
A minimal normal form for DNA expressions,
*Fundamenta Informaticae*,
**123**(2), 2013, 227-243,

respectively.

You may refer to the report as R. van Vliet: All about a Minimal Normal Form for DNA Expressions, Technical Report 2011-03, Leiden Institute of Advanced Computer Science, Leiden University (2011).

*
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.
*

The paper is available here (as pdf). You can also find the paper directly at the publisher's website, when you follow this link. Note that in this paper, we sometimes use terminology which is different from the one in the original DNA 10 paper and the technical report 2004-03 below.

You may refer to the paper as

R. van Vliet, H.J. Hoogeboom, G. Rozenberg:
The construction of minimal DNA expressions,
*Natural Computing*,
**5**(2), May 2006, 127-149.

*
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: what is their length, how are they constructed,
how many of them are there,
and how can they be characterized.
*

The paper is available here (as pdf). You can also find the paper directly at the publisher's website, when you follow this link.

You may refer to the paper as

R. van Vliet, H.J. Hoogeboom, G. Rozenberg:
Combinatorial aspects of minimal DNA expressions,
*DNA Computing -- 10th International Workshop on DNA Computing,
DNA10, Milan, Italy, June 7-10, 2004 -- Revised Selected Papers*,
Lecture Notes in Computer Science **3384**
(C. Ferretti, G. Mauri, C. Zandron, eds.),
Springer-Verlag, Berlin (2005), 375-388.

There are two differences between the first version of the technical report and the final version. On 2 April, 2004, one reference has been removed from the list of references. It was not referred to anyway. On 20 July, 2011, the proof of a certain property has been removed. The report also contained (and still contains) another proof of the same property.

You may refer to the report as R. van Vliet: Combinatorial Aspects of Minimal DNA Expressions (ext.), Technical Report 2004-03, Leiden Institute of Advanced Computer Science, Leiden University (2004).

Questions and comments can be sent to
Rudy van Vliet:
*rvvliet@liacs.nl*.

Last modified: 11 December, 2015
- **http://www.liacs.leidenuniv.nl/~vlietrvan1/dnaexpressions/**