Further remarks on DNA overlap assembly

Abstract The operation of overlap assembly was defined by Csuhaj-Varju, Petre, and Vaszil as a formal model of the linear self-assembly of DNA strands: The overlap assembly of two strings, xy and yz, which share an “overlap” y, results in the string xyz. This paper continues the exploration of the properties of the overlap assembly operation by investigating closure of various language classes under iterated overlap assembly, and the decidability of the completeness of a language. It also investigates the problem of deciding whether a given string is terminal with respect to a language, and the problem of deciding if a given language can be generated by an overlap assembly operation of two given others.

[1]  M. Sahani,et al.  Algorithmic Self-Assembly of DNA , 2006 .

[2]  Oscar H. Ibarra,et al.  Automata with Reversal-Bounded Counters: A Survey , 2014, DCFS.

[3]  Victor Mitrana,et al.  Superposition Based on Watson–Crick-Like Complementarity , 2006, Theory of Computing Systems.

[4]  Lila Kari,et al.  Coding Properties of DNA Languages , 2001, DNA.

[5]  Neil Immerman.  Nondeterministic Space is Closed Under Complementation , 1988, SIAM J. Comput..

[6]  Ion Petre,et al.  Self-assembly of strings and languages , 2007, Theor. Comput. Sci..

[7]  Alfonso Rodríguez-Patón,et al.  Tissue P systems , 2003, Theor. Comput. Sci..

[8]  Grzegorz Rozenberg,et al.  String Tile Models for DNA Computing by Self-Assembly , 2000, DNA Computing.

[9]  Brenda S. Baker,et al.  Reversal-Bounded Multipushdown Machines , 1974, J. Comput. Syst. Sci..

[10]  Seymour Ginsburg,et al.  The Equivalence of Stack Counter Acceptors and Quasi-Realtime Acceptors , 1974, J. Comput. Syst. Sci..

[11]  Tadao Kasami.  A Note on Computing Time for Recognition of Languages Generated by Linear Grammars , 1967, Inf. Control..

[12]  Victor Mitrana,et al.  Some Remarks on Superposition Based on Watson-Crick-Like Complementarity , 2009, Developments in Language Theory.

[13]  Giuditta Franco,et al.  A Polymerase Based Algorithm for SAT , 2005, ICTCS.

[14]  Carlo Laudanna,et al.  DNA Recombination by XPCR , 2005, DNA.

[15]  Victor Mitrana,et al.  On Some Algorithmic Problems Regarding the Hairpin Completion , 2006, Electron. Notes Discret. Math..

[16]  Seymour Ginsburg,et al.  One-way stack automata , 1967, JACM.

[17]  P D Kaplan,et al.  Parallel overlap assembly for the construction of computational DNA libraries. , 1997, Journal of theoretical biology.

[18]  Sheila A. Greibach.  A Note on the Recognition of One Counter Languages , 1975, RAIRO Theor. Informatics Appl..

[19]  Vincenzo Manca,et al.  Algorithmic applications of XPCR , 2011, Natural Computing.

[20]  M. Minsky.  Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines , 1961 .

[21]  Róbert Szelepcsényi,et al.  The method of forced enumeration for nondeterministic automata , 1988, Acta Informatica.

[22]  Carlo Laudanna,et al.  DNA Extraction by XPCR , 2004, DNA.

[23]  Victor Mitrana,et al.  Hairpin Completion Versus Hairpin Reduction , 2007, CiE.

[24]  Oscar H. Ibarra,et al.  Reversal-Bounded Multicounter Machines and Their Decision Problems , 1978, JACM.

[25]  Virginia Vassilevska Williams,et al.  Multiplying matrices faster than coppersmith-winograd , 2012, STOC '12.

[26]  Vincenzo Manca,et al.  Computing by polymerase chain reaction. , 2008, Mathematical biosciences.

[27]  Lila Kari,et al.  A Formal Language Model of DNA Polymerase Enzymatic Activity , 2015, Fundam. Informaticae.

[28]  Hartmut Ehrig,et al.  Formal and Natural Computing , 2002, Lecture Notes in Computer Science.

[29]  Paola Bonizzoni,et al.  Existence of constants in regular splicing languages , 2015, Inf. Comput..

[30]  Oscar H. Ibarra,et al.  On the overlap assembly of strings and languages , 2017, Natural Computing.

[31]  Alfonso Rodríguez-Patón,et al.  A tissue P system and a DNA microfluidic device for solving the shortest common superstring problem , 2005, Soft Comput..

[32]  Lila Kari,et al.  Codes, Involutions, and DNA Encodings , 2002, Formal and Natural Computing.

[33]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[34]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[35]  P D Kaplan,et al.  DNA solution of the maximal clique problem. , 1997, Science.

[36]  Erik Winfree,et al.  Universal computation via self-assembly of DNA: Some theory and experiments , 1996, DNA Based Computers.

[37]  Oscar H. Ibarra,et al.  On the containment and equivalence problems for two-way transducers , 2012, Theor. Comput. Sci..

[38]  L F Landweber,et al.  Molecular computation: RNA solutions to chess problems , 2000, Proc. Natl. Acad. Sci. USA.

[39]  L F Landweber,et al.  Chess games: a model for RNA based computation. , 1999, Bio Systems.

[40]  W. Stemmer.  DNA shuffling by random fragmentation and reassembly: in vitro recombination for molecular evolution. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Steffen Kopecki.  On iterated hairpin completion , 2011, Theor. Comput. Sci..