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Encyclopedia of Complexity and Systems Science pp 1–21Cite as

Mechanical Computing: The Computational Complexity of Physical Devices

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Abstract

This chapter overviews a wide variety of mechanical devices used for computation. The history of mechanical computing devices is also overviewed. Also discussed are lower bounds on the computational resources required to simulate a mechanical system observing given physical laws.

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References

  • Adamatzky AI (1996) On the particle-like waves in the discrete model of excitable medium. Neural Netw World 1:3–10

    Google Scholar 

  • Adamatzky AI (1998a) Universal dynamical computation in multidimensional excitable lattices. Int J Theory Phys 37:3069–3108

    Article  MathSciNet  MATH  Google Scholar 

  • Adamatzky AI (1998b) Chemical processor for computation of voronoi diagram. Adv Mater Opt Electron 6(4):191–196

    Google Scholar 

  • Adamatzky A (ed) (2001) Collision-based computing. Springer, London

    MATH  Google Scholar 

  • Adamatzky A, De Lacy CB, Asai T (2005) Reaction-diffusion computers. Elsevier, New York. isbn:0444520422

    Google Scholar 

  • Adleman LM (1994) Molecular computation of solutions to combinatorial problems. Science 266(11):1021–1024

    Article  ADS  Google Scholar 

  • Adleman L (1998) Computing with DNA. Sci Am 279(2):34–41

    Article  Google Scholar 

  • Babbage C (1822) On machinery for calculating and printing mathematical tables. Edinb Philos J. In: Jameson R, Brewster D (eds) vol VII. Archibald Constable, Edinburgh, pp 274–281

    Google Scholar 

  • Babbage C (1825) Observations on the application of machinery to the computation of mathematical tables. Phil Mag J LXV:311–314. London: Richard Taylor

    Google Scholar 

  • Babbage C (1826) On a method of expressing by signs the action of machinery. Philos Trans R Soc Lond 116(Part III):250–265

    Article  Google Scholar 

  • Bath J, Turberfield AJ (2007) DNA nanomachines. Nat Nanotechnol 2:275–284

    Article  ADS  Google Scholar 

  • Benioff P (1982) Quantum mechanical models of Turing machines that dissipate no energy. Phys Rev Lett 48:1581

    Article  ADS  MathSciNet  Google Scholar 

  • Bennett CH (1973) Logical reversibility of computation. IBM J Res Dev 17(6):525–532

    Article  MathSciNet  MATH  Google Scholar 

  • Bennett CH (1982) The thermodynamics of computation – a review. Int J Theor Phys 21(12):905–940

    Article  Google Scholar 

  • Bennett CH (2003) Notes on Landauer’s principle, reversible computation, and Maxwell’s demon. Stud Hist Philos Mod Phys 34:501–510. eprint physics/0210005

    Article  MathSciNet  MATH  Google Scholar 

  • Berger R (1966) The undecidability of the domino problem. Mem Am Math Soc 66:1–72

    MathSciNet  MATH  Google Scholar 

  • Bernal JD (1964) The structure of liquids. Proc R Soc Lond Ser A 280:299

    Article  ADS  Google Scholar 

  • Blum L, Cucker F, Shub M, Smale S (1996) Complexity and real computation: a manifesto. Int J Bifurc Chaos 6(1):3–26. World Scientific, Singapore

    Article  MathSciNet  MATH  Google Scholar 

  • Boole G (1847) Mathematical analysis of logic: the mathematical analysis of logic: Being an essay towards a calculus of deductive reasoning, pamphlet

    Google Scholar 

  • Boole G (1854) An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities. Macmillan, London

    Book  MATH  Google Scholar 

  • Bragg L, Lomer WM (1948) A dynamical model of a crystal structure II. Proc R Soc A 196:171–181

    Article  ADS  Google Scholar 

  • Bragg L, Nye JF (1947) A dynamical model of a crystal structure. Proc R Soc A 190:474–481

    Article  ADS  Google Scholar 

  • Bush V (1931) The differential analyzer: a new machine for solving differential equations. J Frankl Inst 212:447

    Article  MATH  Google Scholar 

  • Canny J (1988) Some algebraic and geometric computations in PSPACE. In: Cole R (ed) Proceedings of the 20th annual ACM symposium on the theory of computing. ACM Press, Chicago, pp 460–467

    Google Scholar 

  • Canny J, Reif JH (1987) New lower bound techniques for robot motion planning problems. In: 28th annual IEEE symposium on foundations of computer science, Los Angeles, pp 49–60

    Google Scholar 

  • Canny J, Donald B, Reif JH, Xavier P (1988) On the complexity of kinodynamic planning. In: 29th annual IEEE symposium on foundations of computer science, White Plains, pp 306–316. Published as Kinodynamic motion planning J ACM 40(5): 1048–1066 (1993)

    Google Scholar 

  • Chandran H, Gopalkrishnan N, Reif J (2013) In: Mavroidis C, Ferreira A (eds) DNA nanoRobotics, chapter, nanorobotics: current approaches and techniques. Springer, New York, pp 355–382. ISBN 13 : 9781461421184, ISBN 10 : 1461421187

    Google Scholar 

  • Chase GC (1980) History of mechanical computing machinery. IEEE Ann Hist Comput 2(3):198–226

    Article  MathSciNet  MATH  Google Scholar 

  • Cohen IB, Welch GW (1999) Makin’ numbers: Howard Aiken and the computer. MIT Press, Cambridge, MA

    Google Scholar 

  • Corcoran SG, Colton RJ, Lilleodden ET, Gerberich WW (1997) Phys Rev B 190:474

    Google Scholar 

  • Crescenzi P, Papadimitriou CH (1995) Reversible simulation of space-bounded computations. Theor Comput Sci 143(1):159–165

    Article  MathSciNet  MATH  Google Scholar 

  • Danial R, Woo SS, Turicchia L, Sarpeshkar R (2011) Analog transistor models of bacterial genetic circuits. In: Proceedings of the 2011 I.E. biological circuits and systems (BioCAS) conference, San Diego, pp 333–336

    Google Scholar 

  • Daniel R, Rubens J, Sarpeshkar R, Lu T (2013) Synthetic analog computation in living cells. Nature. doi:10.1038/nature12148

    Google Scholar 

  • Davis M (2000) The universal computer: the road from Leibniz to Turing. Norton Press, Norton

    MATH  Google Scholar 

  • Deutsch D (1985) Quantum theory, the church-Turing principle and the universal quantum computer. Proc R Soc Lond A400:97–117

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Dolev S, Fitoussi H (2010) Masking traveling beams: optical solutions for NP-complete problems, trading space for time. Theor Comput Sci 411:837–853

    Article  MathSciNet  MATH  Google Scholar 

  • Engineering Research Associates Staff (1950) High-speed computing devices. McGraw-Hill Book, New York City

    MATH  Google Scholar 

  • Feynman RP (1963) “ratchet and pawl”, chapter 46. In: Feynman RP, Leighton RB, Sands M (eds) The Feynman lectures on physics, vol 1. Addison-Wesley, Reading

    Google Scholar 

  • Feynman RP (1982) Simulating physics with computers. Int J Theor Phys 21(6/7):467–488

    Article  MathSciNet  Google Scholar 

  • Finney JL (1970) Random packings and the structure of simple liquids. I The geometry of random close packing Proc R Soc Lond A Math Phys Sci 319(1539):479–493

    Article  Google Scholar 

  • Fisher EG (1911) Tide-predicting machine. Eng News 66:69–73

    Google Scholar 

  • Fredkin E, Toffoli T (1982) Conservative logic. Int J Theory Phys 21:219–253

    Article  MathSciNet  MATH  Google Scholar 

  • Freeth T, Bitsakis Y, Moussas X, Seiradakis JH, Tselikas A, Mangou H, Zafeiropoulou M, Hadland R, Bate D, Ramsey A, Allen M, Crawley A, Hockley P, Malzbender T, Gelb D, Ambrisco W, Edmunds MG (2006) Decoding the ancient Greek astronomical calculator known as the Antikythera mechanism. Nature 444:587–591

    Article  ADS  Google Scholar 

  • Goliaei S, Foroughmand-Araabi M (2013) Light ray concentration reduces the complexity of the wavelength-based machine on PSPACE languages, unpublished manuscript

    Google Scholar 

  • Goliaei S, Jalili S (2009) An optical wavelength-based solution to the 3-SAT problem. In: Dolev S, Oltean M (eds) Optical supercomputing, Lecture notes in computer science, vol, vol 5882, pp 77–85

    Chapter  Google Scholar 

  • Goliaei S, Jalili S (2012) An optical wavelength-based computational machine. Unconventional computation and natural computation lecture notes in computer science, vol 7445, pp 94–105. Also, Int J Unconv Comput (in press)

    Google Scholar 

  • Grunbaum S, Branko SGC (1987) Tilings and patterns, chapter 11. H Freeman, San Francisco

    MATH  Google Scholar 

  • Gruska J (1999) Quantum computing. McGraw-Hill, New York

    MATH  Google Scholar 

  • Haist T, Osten W (2007) An optical solution for the traveling salesman problem. Opt Express 15(16):10473–10482

    Article  ADS  Google Scholar 

  • Hamer D, Sullivan G, Weierud F (1998) Enigma variations: an extended family of machines. Cryptologia 22(3):211–229

    Article  Google Scholar 

  • Hartree DR (1950) Calculating instruments and machines. Cambridge University Press, London

    MATH  Google Scholar 

  • Henrici (1894) On a new harmonic analyzer, Phil Mag 38:110

    Google Scholar 

  • Hopcroft JE, Schwartz JT, Sharir M (1984) On the complexity of motion planning for multiple independent objects: PSPACE hardness of the warehouseman’s problem. Int J Robot Res 3(4):76–88

    Article  Google Scholar 

  • Horsburgh EM (1914) Modern instruments of calculation. G. Bell & Sons, London, p 223

    MATH  Google Scholar 

  • Jaeger G (2006) Quantum information: an overview. Springer, Berlin

    Google Scholar 

  • Jakubowski MH, Steiglitz K, Squier R (1998) State transformations of colliding optical solitons and possible application to computation in bulk media. Phys Rev E58:6752–6758

    ADS  Google Scholar 

  • Jakubowski MH, Steiglitz K, Squier R (2001) Computing with solitons: a review and prospectus, collision-based computing. Springer, London, pp 277–297

    MATH  Google Scholar 

  • Jevons WS (1870) On the mechanical performance of logical inference. Philos Trans R Soc 160(Part II):497–518

    Article  Google Scholar 

  • Jevons SW (1873) The principles of science; a treatise on logic and scientific method. Macmillan, London

    MATH  Google Scholar 

  • Kelvin L (1878) Harmonic analyzer and synthesizer. Proc R Soc 27:371

    Article  Google Scholar 

  • Knott CG (ed) (1915) Napier tercentenary memorial volume. Published for the Royal Society of Edinburgh by Longmans, Green, London

    MATH  Google Scholar 

  • Landauer R (1961) Irreversibility and heat generation in the computing process. IBM J Res Dev 5:183

    Article  MathSciNet  MATH  Google Scholar 

  • Lehmer DH (1928) The mechanical combination of linear forms. Am Math Mon 35:114–121

    Article  MathSciNet  MATH  Google Scholar 

  • Lenstra AK, Shamir A (2000) Analysis and optimization of the TWINKLE factoring device, proc. Eurocrypt 2000, LNCS 1807. Springer, Heidelberg, pp 35–52

    Google Scholar 

  • Lewis HR, Papadimitriou CH (1981) Elements of the theory of computation. Prentice-Hall, Upper Saddle River, pp 296–300. and 345–348

    Google Scholar 

  • Lewis HR, Papadimitriou CH (1997) Elements of the theory of computation, 2nd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Li M, Vitanyi P (1996) Reversibility and adiabatic computation: trading time and space for energy. Proc R Soc Lond Ser A 452:769–789. (Online preprint quant-ph/9703022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Lindgren M (1990) Glory and failure: difference engines of Johann Muller, Charles Babbage and Georg and Edvard Scheutz. MIT Press, Cambridge, MA

    Google Scholar 

  • Lovelace A, translation of “Sketch of the Analytical Engine” by L. F. Menabrea with Ada's notes and extensive commentary. Ada Lovelace (1843) Sketch of the analytical engine invented by Charles Babbage. Esq Scientific Memoirs 3:666–731

    Google Scholar 

  • Ludgate P (1909–1910) On a proposed analytical engine. Sci Proc Roy Dublin Soc 12:77–91

    Google Scholar 

  • Madou MJ (2002) Fundamentals of microfabrication: the science of miniaturization, 2nd edn. CRC Publishers, Boca Raton

    Google Scholar 

  • Magnasco MO (1997) Chemical kinetics is Turing universal. Phys Rev Lett 78:1190–1193

    Article  ADS  Google Scholar 

  • Mao C, LaBean TH, Reif JH, Seeman NC (2000) Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407:493–495

    Article  ADS  Google Scholar 

  • Martin E (1992) The calculating machines. The MIT Press, Cambridge, MA

    Google Scholar 

  • Miller D (1916) The Henrici harmonic analyzer and devices for extending and facilitating its use. J Franklin Inst 181:51–81 and 182:285–322

    Article  Google Scholar 

  • Moore C (1990) Undecidability and unpredictability in dynamical systems. Phys Rev Lett 64:2354–2357

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Moore C (1991) Generalized shifts: undecidability and unpredictability in dynamical systems. Nonlinearity 4:199–230

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • de Morin H (1913) Les appareils d’intégration: intégrateurs simples et composés; planimètres; intégromètres; intégraphes et courbes intégrales; analyse harmonique et analyseurs. Gauthier-Villars Publishers, Paris

    MATH  Google Scholar 

  • Munakata T, Sinha S, Ditto WL (2002) Chaos computing: implementation of fundamental logical gates by chaotic elements. IEEE Trans Circ Syst-I Fundam Theory Appl 49(11):1629–1633

    Article  MathSciNet  Google Scholar 

  • Muntean O, Oltean M (2009) Deciding whether a linear diophantine equation has solutions by using a light-based device. J Optoelectron Adv Mater 11(11):1728–1734

    Google Scholar 

  • Napier J (1614) Mirifici logarithmorum canonis descriptio (the description of the wonderful canon of logarithms). Hart, Edinburgh

    Google Scholar 

  • Nielsen M, Chuang I (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Norman JM (ed) (2002) The origins of cyberspace: from Gutenberg to the internet: a sourcebook on the history of information technology. Norman Publishing, Novato

    Google Scholar 

  • Oltean M (2008) Solving the Hamiltonian path problem with a light-based computer. Nat Comput 6(1):57–70

    Article  MathSciNet  MATH  Google Scholar 

  • Oltean M, Muntean O (2008) Exact cover with light. New Gener Comput 26(4):329–346

    Article  MATH  Google Scholar 

  • Oltean M, Muntean O (2009) Solving the subset-sum problem with a light-based device. Nat Comput 8(2):321–331

    Article  MathSciNet  MATH  Google Scholar 

  • Oughtred W (1632) Circles of proportion and the horizontal instrument. Translated and Published by William Forster, London

    Google Scholar 

  • Pascal E (1645) Lettre dédicatoire à Monseigneur le Chancelier sur le sujet de la machine nouvellement inventée par le sieur B. P pour faire toutes sortes d’opérations d’arithmétique par un mouvement réglé sans plume ni jetons, suivie d’un avis nécessaire à ceux qui auront curiosité de voir ladite machine et de s’en servir

    Google Scholar 

  • Plummer D, Dalton LJ, Peter F (1999) The recodable locking device. Commun ACM 42(7):83–87

    Article  Google Scholar 

  • Reif JH (1979) Complexity of the mover’s problem and generalizations. In: 20th Annual IEEE symposium on foundations of computer science, San Juan, Puerto Rico, pp 421–427. Also appearing in Chapter 11 in Planning, geometry and complexity of robot motion. Schwartz J (ed) Ablex Pub, Norwood, pp 267–281 (1987)

    Google Scholar 

  • Reif JH (2009a) Quantum information processing: algorithms, technologies and challenges, invited chapter. In: Eshaghian-Wilner MM (ed) Nano-scale and bio-inspired computing. Wiley, Hoboken

    Google Scholar 

  • Reif JH (2009b) Mechanical computation: it’s computational complexity and technologies, invited chapter. In: Meyers RA (ed) Encyclopedia of complexity and system science. Unconventional Computing (Section Editor: Andrew Adamatzky). Springer, New York, ISBN: 978-0-387-75888-6

    Google Scholar 

  • Reif JH, LaBean TH (2007) Autonomous programmable biomolecular devices using self-assembled DNA nanostructures, communications of the ACM (CACM), Special Section entitled “New Computing Paradigms (edited by Toshinori Munakata)

    Google Scholar 

  • Reif JH, LaBean TH (2009) Nanostructures and autonomous devices assembled from DNA. Invited chapter. In: Eshaghian-Wilner MM (ed) Nano-scale and bio-inspired computing. Wiley, Hoboken

    Google Scholar 

  • Reif JH, Sahu S (2008) Autonomous programmable DNA nanorobotic devices using DNAzymes, 13th international meeting on DNA computing (DNA 13), Memphis, June 4–8, 2007. In: Garzon M, Yan H (eds) DNA computing: DNA13, Springer-Verlag lecture notes for computer science (LNCS), vol 4848. Springer, Berlin, pp 66–78. Published in Special Journal Issue on Self-Assembly, Theoretical Computer Science (TCS) 410(15):1428–1439 (2009)

    Chapter  Google Scholar 

  • Reif JH, Sharir M (1985) Motion planning in the presence of moving obstacles. In: 26th annual IEEE symposium on foundations of computer science, Portland, pp 144–154. Published in Journal of the ACM (JACM) 41:4, pp 764–790 (1994)

    Google Scholar 

  • Reif JH, Sun Z (1998) The computational power of frictional mechanical systems. In: Third international workshop on algorithmic foundations of robotics, (WAFR98), Pub. by A. K. Peters Ltd, Houston, pp 223–236. Published as On frictional mechanical systems and their computational power, SIAM Journal of Computing(SICOMP) 32(6):1449–1474 (2003)

    Google Scholar 

  • Reif JH, Wang H (1998) The complexity of the two dimensional curvature-constrained shortest-path problem. In: Third international workshop on algorithmic foundations of robotics (WAFR98), Pub. by A. K. Peters Ltd, Houston, pp 49–57

    Google Scholar 

  • Reif JH, Tygar D, Yoshida A (1990) The computability and complexity of optical beam tracing. 31st annual IEEE symposium on foundations of computer science, St. Louis, pp 106–114. Published as The computability and complexity of ray tracing in discrete & computational geometry 11:265–287 (1994)

    Google Scholar 

  • Reif J, Chandran H, Gopalkrishnan N, LaBean T (2012) Self-assembled DNA nanostructures and DNA devices. Invited chapter 14. In: Cabrini S, Kawata S (eds) Nanofabrication handbook. CRC Press, Taylor and Francis Group, New York, pp 299–328. isbn13:9781420090529, isbn10: 1420090526

    Chapter  Google Scholar 

  • Rothemund PWK (2000) Using lateral capillary forces to compute by self-assembly. Proc Natl Acad Sci USA 97:984–989

    Article  ADS  Google Scholar 

  • Rothemund PWK (2006) Folding DNA to create nanoscale shapes and patterns. Nature 440:297–302

    Article  ADS  Google Scholar 

  • Rothemund PWK, Papadakis N, Winfree E (2004) Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol 2(12): electronic pub. e424. doi:10.1371/journal.pbio.0020424

  • Schwartz JT, Sharir M (1983) On the piano movers’ problem: I. The case of a two-dimensional rigid polygonal body moving amidst polygonal barriers. Commun Pure Appl Math 36:345–398

    Article  MathSciNet  MATH  Google Scholar 

  • Seeman NC (2004) Nanotechnology and the double helix. Sci Am 290(6):64–75

    Article  Google Scholar 

  • Senum P, Riedel M (2011) Rate-independent constructs for chemical computation. PLoS One 6(6):e21414

    Article  ADS  Google Scholar 

  • Shamir A (1999) Factoring large numbers with the TWINKLE device, cryptographic hardware and embedded systems (CHES) 1999, LNCS 1717, 2-12. Springer, Heidelberg

    Google Scholar 

  • Shamir A (n.d.) Method and apparatus for factoring large numbers with optoelectronic devices, patent 475920, filed 12/30/1999 and awarded 08/05/2003

    Google Scholar 

  • Shannon C (1938) A symbolic analysis of relay and switching circuits. Trans Am Inst Electr Eng 57:713–719

    Article  Google Scholar 

  • Shapiro E (1999) A mechanical turing machine: blueprint for a biomolecular computer. In: Fifth international meeting on DNA-based computers at the Massachusetts Institute of Technology, Proc. DNA Based Computers V: Cambridge

    Google Scholar 

  • Sinha S, Ditto W (1999) Computing with distributed chaos. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Top 60(1):363–377

    Google Scholar 

  • Soloveichik D, Cook M, Winfree E, Bruck J (2008) Computation with finite stochastic chemical reaction networks. Nat Comput 7(4):615–633

    Article  MathSciNet  MATH  Google Scholar 

  • Soloveichik D, Seelig G, Winfree E (2010) DNA as a universal substrate for chemical kinetics. Proc Natl Acad Sci 107:5393–5398

    Article  ADS  Google Scholar 

  • Soroka WA (1954) Analog methods in computation and simulation. McGraw-Hill, New York

    MATH  Google Scholar 

  • Squier R, Steiglitz K (1994) Programmable parallel arithmetic in cellular automata using a particle model. Complex Syst 8:311–323

    MathSciNet  MATH  Google Scholar 

  • Svoboda A (1948) Computing mechanisms and linkages. McGraw-Hill, New York

    Google Scholar 

  • Swade D (1991) Charles Babbage and his calculating engines. Michigan State University Press, East Lansing

    Google Scholar 

  • Tate SR, Reif JH (1993) The complexity of N-body simulation. In: Proceedings of the 20th annual colloquium on automata, languages and programming (ICALP’93), Lund, pp 162–176

    Google Scholar 

  • Thomson W (later known as Lord Kelvin) (1878) Harmonic analyzer. Proc R Soc Lond 27:371–373

    Google Scholar 

  • Turck JAV (1921) Origin of modern calculating machines. The Western Society of Engineers, Chicago

    Google Scholar 

  • Turing A (1937) On computable numbers, with an application to the Entscheidungs problem. In: Proceedings of the London mathematical society, second series, vol 42, London, pp 230–265. Erratum in vol 43, pp 544–546

    Google Scholar 

  • da Vinci L (1493) Codex Madrid I

    Google Scholar 

  • Wang H (1963) Dominoes and the AEA case of the decision problem. In: Fox J (ed) Mathematical theory of automata. Polytechnic Press, Brooklyn, pp 23–55

    Google Scholar 

  • Winfree E, Yang X, Seeman NC (1996) Universal computation via self-assembly of DNA: some theory and experiments, DNA based computers II, volume 44 of DIMACS. American Mathematical Society, Providence, pp 191–213

    MATH  Google Scholar 

  • Winfree E, Liu F, Wenzler LA, Seeman NC (1998) Design and self-assembly of two-dimensional DNA crystals. Nature 394:539–544

    Article  ADS  Google Scholar 

  • Wolfram S (1984) Universality and complexity in cellular automata. Physica D10:1–35

    ADS  MathSciNet  MATH  Google Scholar 

  • Woods D, Naughton TJ (2009) Optical computing. Appl Math Comput 215(4):1417–1430

    MathSciNet  MATH  Google Scholar 

  • Xia Y, Whitesides GM (1998) Soft lithography. Ann Rev Mater Sci 28:153–184

    Article  ADS  Google Scholar 

  • Yan H, LaBean TH, Feng L, Reif JH (2003a) Directed nucleation assembly of barcode patterned DNA lattices. Proc Natl Acad Sci U S A 100(14):8103–8108

    Article  ADS  Google Scholar 

  • Yan H, Feng L, LaBean TH, Reif J (2003b) DNA nanotubes, parallel molecular computations of pairwise exclusive-or (XOR) using DNA “string tile” self-assembly. J Am Chem Soc (JACS) 125(47):14246–14247

    Article  Google Scholar 

  • Yin P, Yan H, Daniel XG, Turberfield AJ, Reif JH (2004) A unidirectional DNA walker moving autonomously along a linear track. Angew Chem Int Ed 43(37):4906–4911

    Article  Google Scholar 

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  1. Department of Computer Science, Duke University, 308 Research Drive 90129 D101 LSRC Building, Durham, NC, 27708, USA

    John H. Reif

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  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Reif, J.H. (2017). Mechanical Computing: The Computational Complexity of Physical Devices. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_325-4

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  1. Latest

    Mechanical Computing: The Computational Complexity of Physical Devices
    Published:
    29 April 2017

    DOI: https://doi.org/10.1007/978-3-642-27737-5_325-4

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    Mechanical Computing: The Computational Complexity of Physical Devices
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    17 September 2015

    DOI: https://doi.org/10.1007/978-3-642-27737-5_325-3

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