title: Computing exponentially faster: implementing a non-deterministic universal Turing machine using DNA.
abstract: The theory of computer science is based around universal Turing machines (UTMs): abstract machines able to execute all possible algorithms. Modern digital computers are physical embodiments of classical UTMs. For the most important class of problem in computer science, non-deterministic polynomial complete problems, non-deterministic UTMs (NUTMs) are theoretically exponentially faster than both classical UTMs and quantum mechanical UTMs (QUTMs). However, no attempt has previously been made to build an NUTM, and their construction has been regarded as impossible. Here, we demonstrate the first physical design of an NUTM. This design is based on Thue string rewriting systems, and thereby avoids the limitations of most previous DNA computing schemes: all the computation is local (simple edits to strings) so there is no need for communication, and there is no need to order operations. The design exploits DNA's ability to replicate to execute an exponential number of computational paths in P time. Each Thue rewriting step is embodied in a DNA edit implemented using a novel combination of polymerase chain reactions and site-directed mutagenesis. We demonstrate that the design works using both computational modelling andin vitromolecular biology experimentation: the design is thermodynamically favourable, microprogramming can be used to encode arbitrary Thue rules, all classes of Thue rule can be implemented, and non-deterministic rule implementation. In an NUTM, the resource limitation is space, which contrasts with classical UTMs and QUTMs where it is time. This fundamental difference enables an NUTM to trade space for time, which is significant for both theoretical computer science and physics. It is also of practical importance, for to quote Richard Feynman 'there's plenty of room at the bottom'. This means that a desktop DNA NUTM could potentially utilize more processors than all the electronic computers in the world combined, and thereby outperform the world's current fastest supercomputer, while consuming a tiny fraction of its energy.
authors.affiliation: SYNBIOCHEM, Manchester Institute of Biotechnology, University of Manchester, Manchester, UK.|School of Chemistry, University of Manchester, Manchester, UK.
authors.forename: Andrew
authors.initials: A
authors.lastname: Currin
authors.affiliation: School of Computer Science, University of Manchester, Manchester, UK.
authors.forename: Konstantin
authors.initials: K
authors.lastname: Korovin
authors.affiliation: Manchester Institute of Biotechnology, University of Manchester, Manchester, UK.
authors.forename: Maria
authors.initials: M
authors.lastname: Ababi
authors.affiliation: School of Computer Science, University of Manchester, Manchester, UK.
authors.forename: Katherine
authors.initials: K
authors.lastname: Roper
authors.affiliation: SYNBIOCHEM, Manchester Institute of Biotechnology, University of Manchester, Manchester, UK.|School of Chemistry, University of Manchester, Manchester, UK.
authors.forename: Douglas B
authors.initials: DB
authors.lastname: Kell
authors.affiliation: Manchester Institute of Biotechnology, University of Manchester, Manchester, UK.|Faculty of Biology, Medicine and Health, University of Manchester, Manchester, UK.
authors.forename: Philip J
authors.initials: PJ
authors.lastname: Day
authors.affiliation: School of Computer Science, University of Manchester, Manchester, UK ross.king@manchester.ac.uk.|Manchester Institute of Biotechnology, University of Manchester, Manchester, UK.
authors.forename: Ross D
authors.identifier: 0000-0001-7208-4387
authors.initials: RD
authors.lastname: King
mesh_terms: D000465:Algorithms; D039301:Computers, Molecular; D008962:Models, Theoretical
keywords: DNA computing; complexity theory; non-deterministic universal Turing machine