Autonomous Resolution Based on DNA Strand Displacement

We present a computing model based on the technique of DNA strand displacement which performs a chain of logical resolutions with logical formulae in conjunctive normal form. The model is enzymefree and autonomous. Each clause of a formula is encoded in a separate DNA molecule: propositions are encoded assigning a strand to each proposition p, and its complementary strand to the proposition ¬p; clauses are encoded comprising different propositions in the same strand. The model allows to run logic programs composed of Horn clauses by cascading resolution steps and, therefore, possibly function as an autonomous programmable nano-device. This technique can be also used to solve SAT. The resulting SAT algorithm has a linear time complexity in the number of resolution steps, whereas its spatial complexity is exponential in the number of variables of the formula.

[1]  Jacobo Torán,et al.  Space Bounds for Resolution , 2001, Inf. Comput..

[2]  David I. Lewin,et al.  DNA computing , 2002, Comput. Sci. Eng..

[3]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[4]  Brian M. Frezza,et al.  Modular multi-level circuits from immobilized DNA-based logic gates. , 2007, Journal of the American Chemical Society.

[5]  P. Hsieh,et al.  The kinetics of spontaneous DNA branch migration. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Piotr Wasiewicz,et al.  The Inference Based on Molecular Computing , 2000, Cybern. Syst..

[7]  P. Hsieh,et al.  Branch migration through DNA sequence heterology. , 1998, Journal of molecular biology.

[8]  K Sakamoto,et al.  Molecular computation by DNA hairpin formation. , 2000, Science.

[9]  Luca Cardelli.  Strand Algebras for DNA Computing , 2009, DNA.

[10]  Vincenzo Manca.  DNA and Membrane Algorithms for SAT , 2002, Fundam. Informaticae.

[11]  Satoshi Kobayashi,et al.  Horn Clause Computation by Self-assembly of DNA Molecules , 2001, DNA.

[12]  G. Seelig,et al.  DNA as a universal substrate for chemical kinetics , 2010, Proceedings of the National Academy of Sciences.

[13]  R J Lipton,et al.  DNA solution of hard computational problems. , 1995, Science.

[14]  Yasubumi Sakakibara,et al.  DNA Computing and Molecular Programming - 16th International Conference, DNA 16, Hong Kong, China, June 14-17, 2010, Revised Selected Papers , 2011, DNA.

[15]  Alfonso Rodríguez-Patón,et al.  Inference with DNA Molecules , 2010, UC.

[16]  Vincenzo Manca,et al.  A Clause String DNA Algorithm for SAT , 2001, DNA.

[17]  Masami Hagiya,et al.  Chain Reaction Systems Based on Loop Dissociation of DNA , 2005, DNA.

[18]  Lila Kari,et al.  Scalable, Time-Responsive, Digital, Energy-Efficient Molecular Circuits Using DNA Strand Displacement , 2010, DNA.

[19]  Mitsunori Ogihara.  Breadth First Search 3SAT Algorithms for DNA Computers , 1996 .

[20]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[21]  Ehud Shapiro,et al.  Molecular implementation of simple logic programs. , 2009, Nature nanotechnology.

[22]  S. Basu,et al.  A synthetic multicellular system for programmed pattern formation , 2005, Nature.

[23]  Stephen C. West,et al.  Happy Hollidays: 40th anniversary of the Holliday junction , 2004, Nature Reviews Molecular Cell Biology.

[24]  Xiaolong Wang,et al.  Solving the SAT problem using a DNA computing algorithm based on ligase chain reaction , 2008, Biosyst..

[25]  G. Seelig,et al.  Enzyme-Free Nucleic Acid Logic Circuits , 2022 .

[26]  Satoshi Kobayashi,et al.  Horn Clause Computation with DNA Molecules , 1999, J. Comb. Optim..

[27]  Armin Haken,et al.  The Intractability of Resolution , 1985, Theor. Comput. Sci..

[28]  James J. Collins,et al.  A Tunable Genetic Switch Based on RNAi and Repressor Proteins for Regulating Gene Expression in Mammalian Cells , 2007, Cell.

[29]  E. Shapiro,et al.  An autonomous molecular computer for logical control of gene expression , 2004, Nature.

[30]  F. Stahl,et al.  The Holliday junction on its thirtieth anniversary. , 1994, Genetics.