An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Characterizing Regular Languages with Polynomial Densities
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
The syntactic monoid of hairpin-free languages
Acta Informatica
Hairpin Completion Versus Hairpin Reduction
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Finding the Growth Rate of a Regular of Context-Free Language in Polynomial Time
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Two complementary operations inspired by the DNA hairpin formation: Completion and reduction
Theoretical Computer Science
On some algorithmic problems regarding the hairpin completion
Discrete Applied Mathematics
On the Hairpin Completion of Regular Languages
ICTAC '09 Proceedings of the 6th International Colloquium on Theoretical Aspects of Computing
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Information and Computation
Complexity results and the growths of hairpin completions of regular languages
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
On iterated hairpin completion
Theoretical Computer Science
Hairpin structures in DNA words
DNA'05 Proceedings of the 11th international conference on DNA Computing
Language theoretical properties of hairpin formations
Theoretical Computer Science
Iterated hairpin completions of non-crossing words
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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Hairpin completion is an operation on formal languages that has been inspired by hairpin formation in DNA biochemistry and by DNA computing. In this paper we investigate the one- and two-sided hairpin completion of regular languages. We solve an open problem from the literature by showing that the regularity problem for hairpin completions is decidable. Actually, we show that the problem is decidable in polynomial time if the input is specified by DFAs. Furthermore, we prove that the hairpin completion of regular languages is an unambiguous linear context-free language. Beforehand, it was known only that it is linear context-free. Unambiguity is a strong additional property because it allows to compute the growth function or the topological entropy. In particular, we can compare the growth of the hairpin completion with the growth of the defining regular languages. We show that the growth of the hairpin completion is exponential if and only if the growth of the underlying languages is exponential. Even if both growth functions are exponential, they can be as far apart as 2^@Q^(^n^) for the hairpin completion and 2^@Q^(^n^) for the defining regular languages. However, if the hairpin completion is still regular, then the hairpin completion and its underlying language have essentially the same growth and same topological entropy.