Steffen Kopecki

On the Hairpin Completion of Regular Languages

The hairpin completion is a natural operation of formal languages which has been inspired by molecular phenomena in biology and by DNA-computing. The hairpin completion of a regular language is linear context-free and we consider the problem to decide whether the hairpin completion remains regular. This problem has been open since the first formal definition of the operation. In this paper we present a positive solution to this problem. Our solution yields more than decidability because we present a polynomial time procedure. The degree of the polynomial is however unexpectedly high, since in our approach it is more than n 14. Nevertheless, the polynomial time result is surprising, because even if the hairpin completion

On iterated hairpin completion

\mathcal{H}

Binary Pattern Tile Set Synthesis Is NP-Hard

of a regular language L is regular, there can be an exponential gap between the size of a minimal DFA for L and the size of a smallest NFA for

On the iterated hairpin completion

\mathcal{H}

Deciding Whether a Regular Language Is Generated by a Splicing System

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Complexity Results and the Growths of Hairpin Completions of Regular Languages (Extended Abstract)

(Bounded) hairpin completion and its iterated versions are operations on formal languages which have been inspired by hairpin formation in DNA biochemistry. The paper answers two questions asked in the literature about iterated hairpin completion. The first question is whether the class of regular languages is closed under iterated bounded hairpin completion. Here we show that this is true by providing a more general result which applies to all classes of languages which are closed under finite union, intersection with regular sets, and concatenation with regular sets. In particular, all Chomsky classes and all standard complexity classes are closed under iterated bounded hairpin completion. In the second part of the paper we address the question whether the iterated hairpin completion of a singleton is always regular. In contrast to the first question, this one has a negative answer. We exhibit an example of a singleton language whose iterated hairpin completion is not regular: actually, it is not context-free, but context-sensitive.

An investigation into inter- and intragenomic variations of graphic genomic signatures

We solve an open problem, stated in 2008, about the feasibility of designing efficient algorithmic self-assembling systems which produce 2-dimensional colored patterns. More precisely, we show that the problem of finding the smallest tile assembly system which rectilinearly self-assembles an input pattern with 2 colors (i.e., 2-Pats) is

A Formal Language Model of DNA Polymerase Enzymatic Activity

\mathbf {NP}