9 research outputs found
More Structural Characterizations of Some Subregular Language Families by Biautomata
We study structural restrictions on biautomata such as, e.g., acyclicity,
permutation-freeness, strongly permutation-freeness, and orderability, to
mention a few. We compare the obtained language families with those induced by
deterministic finite automata with the same property. In some cases, it is
shown that there is no difference in characterization between deterministic
finite automata and biautomata as for the permutation-freeness, but there are
also other cases, where it makes a big difference whether one considers
deterministic finite automata or biautomata. This is, for instance, the case
when comparing strongly permutation-freeness, which results in the family of
definite language for deterministic finite automata, while biautomata induce
the family of finite and co-finite languages. The obtained results nicely fall
into the known landscape on classical language families.Comment: In Proceedings AFL 2014, arXiv:1405.527
Complexity results and the growths of hairpin completions of regular languages
The hairpin completion is a natural operation on formal languages which has been inspired by molecular phenomena in biology and by DNA-computing. In 2009 we presented a (polynomial time) decision algorithm to decide regularity of the hairpin completion. In this paper we provide four new results:
1.) We show that the decision problem is NL-complete.
2.) There is a polynomial time decision algorithm which runs in time O(n8), this improves our previous results, which provided O(n^{20}).
3.) For the one-sided case (which is closer to DNA computing) the time is O(n2), only.
4.) The hairpin completion of a regular language is unambiguous linear context-free. This result allows to compute the growth (generating function) of the hairpin completion and to compare it with the growth of the underlying regular language
Deciding Regularity of Hairpin Completions of Regular Languages in Polynomial Time
The hairpin completion is an operation on formal languages that has been
inspired by the hairpin formation in DNA biochemistry and by DNA computing. In
this paper we investigate the hairpin completion of regular languages.
It is well known that hairpin completions of regular languages are linear
context-free and not necessarily regular. As regularity of a (linear)
context-free language is not decidable, the question arose whether regularity
of a hairpin completion of regular languages is decidable. We prove that this
problem is decidable and we provide a polynomial time algorithm.
Furthermore, we prove that the hairpin completion of regular languages is an
unambiguous linear context-free language and, as such, it has an effectively
computable growth function. Moreover, we show that the growth of the hairpin
completion is exponential if and only if the growth of the underlying languages
is exponential and, in case the hairpin completion is regular, then the hairpin
completion and the underlying languages have the same growth indicator
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
It Is NL-complete to Decide Whether a Hairpin Completion of Regular Languages Is Regular
The hairpin completion is an operation on formal languages which is inspired
by the hairpin formation in biochemistry. Hairpin formations occur naturally
within DNA-computing. It has been known that the hairpin completion of a
regular language is linear context-free, but not regular, in general. However,
for some time it is was open whether the regularity of the hairpin completion
of a regular language is is decidable. In 2009 this decidability problem has
been solved positively by providing a polynomial time algorithm. In this paper
we improve the complexity bound by showing that the decision problem is
actually NL-complete. This complexity bound holds for both, the one-sided and
the two-sided hairpin completions