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The syntactic monoid of hairpin-free languages

Lila Kari, Kalpana Mahalingam, Gabriel Thierrin
2007 Acta Informatica  
We also give a complete characterization of the syntactic monoid of the language consisting of all hairpin-free words over a given alphabet and illustrate it with an example using the DNA alphabet.  ...  This paper continues the theoretical study of hairpin-free languages. We study algebraic properties of hairpin-free words and hairpins.  ...  These results give thus complete characterization of the syntactic monoid of the language of hairpin-free words over an alphabet. We also discuss the Green's relations for hairpin-free languages.  ... 
doi:10.1007/s00236-007-0041-4 fatcat:wkth6tkuqnanvjc6ntfnsdorbe

WATSON-CRICK BORDERED WORDS AND THEIR SYNTACTIC MONOID

LILA KARI, KALPANA MAHALINGAM
2008 International Journal of Foundations of Computer Science  
We also give a complete characterization of the syntactic monoid of the language consisting of all Watson-Crick bordered words over a given alphabet.  ...  This paper studies a mathematical formalization of a particular case of hairpins, the Watson-Crick bordered words.  ...  In [10] we showed that the elements of the syntactic monoid of the language of all hairpin-free words are idempotents and the monoid is commutative.  ... 
doi:10.1142/s0129054108006200 fatcat:waovhmfbn5dlda6cliyjlu35zu

Language theoretical properties of hairpin formations

Volker Diekert, Steffen Kopecki
2012 Theoretical Computer Science  
This result applies, in particular, to the class of first-order definable languages (which is the class of aperiodic or star-free languages) and it applies to the class of first-order definable languages  ...  We study language theoretical properties of hairpin formations and our new results concern the hairpin completion H κ (L 1 , L 2 ) of two regular languages L 1 and L 2 and the iterated hairpin lengthening  ...  We conjecture that this is the smallest variety of the form V * D containing W.  ... 
doi:10.1016/j.tcs.2011.12.025 fatcat:yivma4fdxzestoyxnfy36rx2ke

Page 1293 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
Ferenc Gécseg and Magnus Steinby, Minimal recognizers and syntactic monoids of DR tree languages (155-167); Tom Head, Visualizing languages using primitive powers (169-180); Juha Honkala, On sparse OL  ...  languages over the binary alphabet (181- 188); Lucian Ilie, On generalized slenderness of context-free lan- guages (189-202); Teruo Imaoka, Prehomomorphisms on locally inverse *-semigroups (203-209); Florentin  ... 

Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081)

Maxime Crochemore, Lila Kari, Mehryar Mohri, Dirk Nowotka, Marc Herbstritt
2011 Dagstuhl Reports  
They occur whenever information is electronically transmitted (as bit streams), when natural language text is spoken or written down (as words over, for example, the latin alphabet), in the process of  ...  This report documents the program and the outcomes of Dagstuhl Seminar 11081 "Combinatorial and Algorithmic Aspects of Sequence Processing".  ...  Problem: estimate the growth of the language of the k-ary RT (k) + -free language. Exponential conjecture (folklore): all these languages have exponential growth. Confirmed by Ochem for k = 3, 4.  ... 
doi:10.4230/dagrep.1.2.47 dblp:journals/dagstuhl-reports/CrochemoreKMN11 fatcat:s3v55bqr4fbdfo5kztirfoljqm

A Categorical Compositional Distributional Modelling for the Language of Life [article]

Yanying Wu, Quanlong Wang
2019 arXiv   pre-print
Since we can think of biological sequences as the "language of life", it is attempting to apply the DisCoCat model on the language of life to see if we can obtain new insights and a better understanding  ...  The Categorical Compositional Distributional (DisCoCat) Model is a powerful mathematical model for composing the meaning of sentences in natural languages.  ...  Coincidently, when the double helix structure of DNA was discovered in the 1950s, linguist Noam Chomsky also developed the revolutionary theory revealing the syntactic structure of natural languages [  ... 
arXiv:1902.09303v3 fatcat:gwvjanqbnbcwzok7r6xv7uukpu

Deciding regularity of hairpin completions of regular languages in polynomial time

Volker Diekert, Steffen Kopecki, Victor Mitrana
2012 Information and Computation  
√ n ) for the hairpin completion and 2 Θ(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.  ...  Acknowledgments The authors thank the anonymous referees for many valuable comments and suggestions which improved the presentation of the results.  ... 
doi:10.1016/j.ic.2012.04.003 fatcat:vbnp6hsr4fgg3pirsrxa2htb2y

DNA Computing — Foundations and Implications [chapter]

Lila Kari, Shinnosuke Seki, Petr Sosík
2012 Handbook of Natural Computing  
The maximality problem of hairpin-free languages is stated as follows: can a given language L ⊆ Σ * , satisfying a certain property (e.g., to be a hairpin-free language), be still extended without loss  ...  For hairpin-free languages it is relatively straightforward to solve the optimal negative design problem: to construct a set of hairpin-free DNA words of a given size, where the words can be chosen from  ... 
doi:10.1007/978-3-540-92910-9_33 fatcat:n3zmhzpj5rgsphmurdophcg234

Algebraic dynamic programming for multiple context-free grammars

Maik Riechert, Christian Höner zu Siederdissen, Peter F. Stadler
2016 Theoretical Computer Science  
We present theoretical foundations, and a practical implementation, that makes the method of Algebraic Dynamic Programming available for Multiple Context-Free Grammars.  ...  This improves on the previous state of the art which required complex code based on hand-written dynamic programming recursions.  ...  The language of G is the set L(G) = {w ∈ A * | Z * ⇒ w}. A 150 language L is a multiple context-free language if there is a MCFG G such that L = L(G).  ... 
doi:10.1016/j.tcs.2016.05.032 fatcat:i4o6bie3pzdlthl567kmvtim4y

Formal language theory of hairpin formations [article]

Steffen Kopecki, Universität Stuttgart, Universität Stuttgart
2011
We show that if the hairpin completion of an aperiodic (i.e., star-free) language is regular, then the hairpin completion is aperiodic, too.  ...  As a by-product of our technique to prove the complexities, we obtain that the hairpin completion of a regular language is actually an unambiguous linear context-free language.  ...  Every variety V induces a variety of languages which consists of all languages whose syntactic monoid belongs to V.  ... 
doi:10.18419/opus-2706 fatcat:uor23tvddzgfvespvvtya2dyzq

Tree adjoining grammars for RNA structure prediction

Yasuo Uemura, Aki Hasegawa, Satoshi Kobayashi, Takashi Yokomori
1999 Theoretical Computer Science  
the subclass, together with some of its language theoretic characterizations.  ...  Then, based on the algorithm, we develop a prediction system and demonstrate the effectiveness of the system by presenting some experimental results obtained from biological data, where free energy evaluation  ...  Acknowledgements The authors are heartly grateful to the referee for many constructive suggestions and comments on the draft of this paper, which greatly improved the readability as well as consistency  ... 
doi:10.1016/s0304-3975(98)00090-5 fatcat:c3fcyprr7jbcbb7wztes5rayga

Page 1938 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
The reduction principle for hierarchies of star-free languages. (Russian Russian summary) 2002b:68047 Silva, Pedro V. see Almeida, Jorge, 2002a:68065 Sokratova, O.  ...  (English summary) (see 2002k:68001 ) — (with Rozenberg, Grzegorz; Yokomori, Takashi) Hairpin languages.  ... 

Strand Algebras for DNA Computing [chapter]

Luca Cardelli
2009 Lecture Notes in Computer Science  
We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures.  ...  components that obey the high-level semantics of the language.  ...  Its basic algebraic laws are the commutative monoid laws of + and 0, where + is the chemical combination symbol and 0 represents the empty solution.  ... 
doi:10.1007/978-3-642-10604-0_2 fatcat:uiwjx3ujargrjeh2pstqgp7p4e

Strand algebras for DNA computing

Luca Cardelli
2010 Natural Computing  
We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures.  ...  components that obey the high-level semantics of the language.  ...  Its basic algebraic laws are the commutative monoid laws of + and 0, where + is the chemical combination symbol and 0 represents the empty solution.  ... 
doi:10.1007/s11047-010-9236-7 fatcat:kundz7lkdnb37ghdoiart4wg3m

Dagstuhl Reports, Volume 1, Issue 2, February 2011, Complete Issue [article]

2011
From an algebraic point of view, the context equivalence problem is exactly the word problem in the syntactic monoid of the language L.  ...  To name one of them, the hairpin completion of a regular language is an unambiguous (linear) context-free language, but the hairpin lengthening may lead to an inherent ambiguous (linear) context-free language  ...  Problem: estimate the growth of the language of the k-ary RT (k) + -free language. Exponential conjecture (folklore): all these languages have exponential growth. Confirmed by Ochem for k = 3, 4.  ... 
doi:10.4230/dagrep.1.2 fatcat:4kh64xsaare75bozj6ltf67dxe
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