Article Outline
Glossary
Definition of the Subject
Introduction
The Computational Complexity of Motion Planning and Simulation of Mechanical Devices
Concrete Mechanical Computing Devices
Future Directions
Acknowledgments
Bibliography
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- Mechanism :
-
A machine or part of a machine that performs a particular task computation: the use of a computer for calculation.
- Computable :
-
Capable of being worked out by calculation, especially using a computer.
- Simulation :
-
The term simulation will be used to denote both the modeling of a physical system by a computer as well as the modeling of the operation of a computer by a mechanical system; the difference will be clear from the context.
Bibliography
Turing A (1937) On Computable Numbers, with an Application to theEntscheidungsproblem. Proc Lond Math Soc, Second Ser, London 42:230–265. Erratum in 43:544–546
Lewis HR, Christos PH (1997) Elements of the Theory of Computation, 2ndedn. Prentice Hall, Upper Saddle River
Landauer R (1961) Irreversibility and heat generation in the computingprocess. IBMJ Res Dev 5:183
Bennett CH (1973) Logical reversibility of computation. IBM J Res Dev17(6):525–532
Li M, Vitanyi P (1996) Reversibility and Adiabatic Computation: Trading Time andSpace for Energy. Proc Roy Soc Lond, Series A 452:769–789. Preprint quant-ph/9703022
Crescenzi P, Christos PH (1995) Reversible simulation of space‐boundedcomputations. Theor Comput Sci 143(1):159–165
Wolfram S (1984) Universality and complexity in cellular automata. Phys D10:1–35
Blum L, Cucker F, Shub M, Smale S (1996) Complexity and Real Computation:A Manifesto. Int J Bifurc Chaos 6(1):3–26
Feynman RP (1982) Simulating physics with computers. Int J Theor Phys21(6–7):467–488
Benioff P (1982) Quantum mechanical models of Turing machines that dissipateno energy. Phys Rev Lett 48:1581
Deutsch D (1985) Quantum theory, the Church–Turing principle and theuniversal quantum computer. Proc Roy Soc A 400:97–117
Gruska J (1999) Quantum Computing. McGraw–Hill,Maidenhead
Nielsen M, Chuang I (2000) Quantum Computation and QuantumInformation. Cambridge University Press, Cambridge
Jaeger G (2006) Quantum Information: An Overview. Springer,Berlin
Reif JH (2007) Quantum Information Processing: Algorithms, Technologies andChallenges In: Eshaghian-Wilner MM (ed) Nano‐scale and Bio‐inspired Computing. Wiley, Malden
Reif JH (1979) Complexity of the Mover’s Problem and Generalizations. 20thAnnual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, October pp 421–427; (1987) In: Schwartz J (ed) Planning,Geometry and Complexity of Robot Motion. Ablex Pub Norwood, NJ, pp 267–281
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, IL, pp 460–467
Schwartz JT, Sharir M (1983) On the piano movers problem: I the case ofa two‐dimensional rigid polygonal body moving amidst polygonal barriers. Comm Pure Appl Math 36:345–398
Hopcroft JE, Schwartz JT, Sharir M (1984) On the Complexity of Motion Planningfor Multiple Independent Objects: PSPACE Hardness of the Warehouseman’s Problem. Int J Robot Res 3(4):76–88
Bennett CH (1982) The thermodynamics of computation –a review. Int J Theor Phys21(12):905–940. http://www.research.ibm.com/people/b/bennetc/bennettc1982666c3d53.pdf
Bennett CH (2003) Notes on Landauer’s principle, reversible computation, andMaxwell’s Demon. Stud History Philos Mod Phys 34:501–510. eprint physics/0210005:http://xxx.lanl.gov/abs/physics/0210005
Adamatzky A (ed) (2001) Collision‐based computing. Springer,London
Squier R, Steiglitz K (1994) Programmable parallel arithmetic in cellularautomata using a particle model. Complex Syst 8:311–323
Fredkin E, Toffoli T (1982) Conservative logic. Int J Theor Phys21:219–253
Adamatzky AI (1996) On the particle‐like waves in the discrete model ofexcitable medium. Neural Netw World 1:3–10
Adamatzky AI (1998) Universal dynamical computation in multidimensionalexcitable lattices. Int J Theor Phys 37:3069–3108
Jakubowski MH, Steiglitz K, Squier R (1998) State transformations of collidingoptical solitons and possible application to computation in bulk media. Phys Rev E58:6752–6758
Jakubowski MH, Steiglitz K, Squier R (2001) Computing with solitons:a review and prospectus, Collision‐based computing. Springer, London, pp 277–297
Feynman RP (1963) In: Feynman RP, Leighton RB, Sands M (eds) Ratchet and Pawl,The Feynman Lectures on Physics, vol 1, Chapter 46. Addison–Wesley, Reading
Shapiro E (1999) A Mechanical Turing Machine: Blueprint fora Biomolecular Computer. Fifth International Meeting on DNA-Based Computers at the Massachusetts Institute of Technology, Proc DNA Based ComputersV. Cambridge, MA, pp 14–16
Reif JH, Sharir M (1994) Motion Planning in the Presence of MovingObstacles. 26th Annual IEEE Symposium on Foundations of Computer Science, Portland, OR, October 1985 pp 144–154; J ACM (JACM)41(4):764–790
Canny J, Reif JH (1987) New Lower Bound Techniques for Robot Motion PlanningProblems. 28th Annual IEEE Symposium on Foundations of Computer Science, Los Angeles, CA, October pp 49–60
Canny J, Donald B, Reif JH, Xavier P (1993) On the Complexity of KinodynamicPlanning. 29th Annual IEEE Symposium on Foundations of Computer Science, White Plains, NY, October (1988) pp 306–316; Kinodynamic MotionPlanning. J ACM 40(5):1048–1066
Reif JH, Wang H (1998) The Complexity of the Two DimensionalCurvature‐Constrained Shortest‐Path Problem. Third International Workshop on Algorithmic Foundations of Robotics (WAFR98). Peters AK Ltd,Houston, pp 49–57
Reif JH, Tygar D, Yoshida A (1994) The Computability and Complexity of OpticalBeam Tracing. 31st Annual IEEE Symposium on Foundations of Computer Science, St Louis, MO, October (1990) pp 106–114; The Computability andComplexity of Ray Tracing. Discrete Comput Geometry 11:265–287
Tate SR, Reif JH (1993) The Complexity of N-body Simulation. Proceedings ofthe 20th Annual Colloquium on Automata, Languages and Programming (ICALP’93), Lund, pp 162–176
Reif JH, Sun Z (2003) The Computational Power of Frictional MechanicalSystems. Third International Workshop on Algorithmic Foundations of Robotics, (WAFR98). Peters AK Ltd, Houston, Texas, Mar 5–7 1998,pp 223–236; On Frictional Mechanical Systems and Their Computational Power. SIAM J Comput (SICOMP)32(6):1449–1474
Moore C (1990) Undecidability and Unpredictability in Dynamical Systems. PhysRev Lett 64:2354–2357
Moore C (1991) Generalized Shifts: Undecidability and Unpredictability inDynamical Systems. Nonlinearity 4:199–230
Munakata T, Sinha S, Ditto WL (2002) Chaos Computing: Implementation ofFundamental Logical Gates by Chaotic Elements. IEEE Trans Circuits Syst-I Fundam Theory Appl 49(11):1629–1633
Sinha S, Ditto (1999) Computing with distributed chaos. Phys Rev E Stat PhysPlasmas Fluids Relat Interdiscip Top 60(1):363–77
Knott CG (ed) (1915) Napier tercentenary memorial volume. The Royal Society ofEdinburgh, Longmans, Green, London
Hartree DR (1950) Calculating Instruments and Machines. Cambridge UniversityPress, Cambridge
Engineering Research Associates Staff (1950) High‐Speed ComputingDevices. McGraw–Hill, New York
Chase GC (1980) History of Mechanical Computing Machinery. Ann Hist Comput2(3):198–226
Martin E (1992) The Calculating Machines. The MIT Press, Cambridge,Massachusetts
Davis M (2000) The Universal Computer: The Road from Leibniz toTuring. Norton, New York
Norman JM (ed) (2002) The Origins of Cyberspace: From Gutenberg to theInternet: a sourcebook on the history of information technology. Norman Publishing, Novato
Horsburgh EM (ed) (1914) Modern Instruments and Methodsof Calculation: a Handbook of the Napier Tercentenary Exhibition, London, G Bell and Sons, Edinburgh, The Royal Society of Edinburgh, p 223. Reprinted 1982
Turck JAV (1921) Origin of Modern Calculating Machines. The Western Society ofEngineers, Chicago
Svoboda A (1948) Computing Mechanisms and Linkages. McGraw–Hill,Columbus
Soroka WA (1954) Analog Methods in Computation andSimulation. McGraw–Hill
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 ancientGreek astronomical calculator known as the Antikythera Mechanism. Nature 444:587–591
de Morin H (1913) Les appariéls d’intégration: intégrateurs simples etcompasés, planimètres, intégromètres, intégraphes et courbes intégrales, analyse harmonique et analyseurs. Gauthier-Villars, Paris,pp 162–171
Thomson W (later known as Lord Kelvin) (1878) Harmonic Analyzer. Proc Roy SocLond 27:371–373
Henrici (1894) Philos Mag 38:110
Lord Kelvin (1878) Harmonic analyzer and synthesizer. Proc Roy Soc27:371
Miller D (1916) The Henrici harmonic analyzer and devices for extending andfacilitating its use. J Franklin Inst 181:51–81; 182:285–322
Fisher EG (1911) Tide‐predicting machine. Eng News66:69–73
Bush V (1931) The differential analyzer: A new machine for solvingdifferential equations. J Franklin Inst 212:447
Bernal JD (1964) The Structure of Liquids. Proc Roy Soc Lond Ser A 280,299
Finney JL (1970) Random Packings and the Structure of Simple Liquids. I TheGeometry of Random Close Packing. Proc Royal Soc London, Ser A, Math Phys Sci 319(1539):479–493
Bragg L, Nye JF (1947) A dynamical model of a crystalstructure. Proc R Soc A 190:474–481
Bragg L, Lomer WM (1948) A dynamical model of a crystal structureII. Proc R Soc A 196:171–181
Corcoran SG, Colton RJ, Lilleodden ET, Gerberich WW (1997) Phys Rev B190:474
Adamatzky A, De Lacy BC, Asai T (2005) Reaction‐DiffusionComputers. Elsevier, Amsterdam
Adamatzky AI (1994) Constructing a discrete generalized Voronoi diagramin reaction‐diffusion media. Neural Netw World 6:635–643
da Vinci L (1493) Codex Madrid I
Napier J (1614) Mirifici logarithmorum cannonis descriptio (the description ofthe wonderful canon of logarithms). Hart, Edinburgh
Oughtred W (1632) Circles of Proportion and the Horizontal Instrument. WilliamForster, London
Pascal E (1645) Lettre dédicatoire à Monseigneur le Chancelier sur le sujet dela machine nouvellement inventée par le sieur BP pour faire toutes sortes d’opérations d’arithmétique par un mouvement réglé sans plume ni jetons, suivied’un avis nécessaire à ceux qui auront curiosité de voir ladite machine et de s’en servir
Babbage C (1822) On Machinery for Calculating and Printing MathematicalTables. Edinburgh Philos J VII:274–281
Babbage C (1822) Observations on the application of machinery to thecomputation of mathematical tables. Memoirs of the Astronomical Society 1:311–314
Babbage C (1826) On a Method of expressing by Signs the Action ofMachinery.Philosophical Trans Royal Soc London 116(III):250–265
Ludgate P (1909) On a proposed analytical engine. Sci Proc Roy Dublin Soc12:77–91
Lindgren M (1990) Glory and Failure: Difference Engines of Johann Muller,Charles Babbage and Georg and Edvard Scheutz. MIT Press, Cambridge
Swade D (1991) Charles Babbage and His Calculating Engines. Michigan StateUniversity Press, East Lensing
Lovelace A (1843) Sketch of the analytical engine invented by CharlesBabbage. Translation of: Sketch of the Analytical Engine by Menabrea LF with Ada’s notes and extensive commentary. Esq Sci Mem3:666–731
Cohen BI, Welch GW (1999) Makin’ Numbers: Howard Aiken and the Computer. MITPress, Cambridge
Boole G (1847) Mathematical Analysis ofLogic. Pamphlet
Boole G (1854) An Investigation of the Laws of Thought, on Which are Foundedthe Mathematical Theories of Logic and Probabilities. Macmillan, Cambridge
Shannon C (1938) A Symbolic Analysis of Relay and SwitchingCircuits. Trans Am Inst Electr Eng 57:713–719
Jevons SW (1870) On the Mechanical Performance of Logical Inference. PhilosTrans Roy Soc, Part II 160:497–518
Jevons SW (1873) The Principles of Science. A Treatise on Logic andScientific Method. Macmillan, London
Hamer D, Sullivan G, Weierud F (1998) Enigma Variations: an Extended Family ofMachines. Cryptologia 22(3):211–229
Lehmer DH (1928) The mechanical combination of linear forms. Am Math Mon35:114–121
Shamir A (1999) Method and apparatus for factoring large numbers withoptoelectronic devices. patent 475920, awarded 08/05/2003
Shamir A (1999) Factoring large numbers with the TWINKLE device. CryptographicHardware and Embedded Systems (CHES) 1999. LNCS, vol 1717. Springer, New York, pp 2–12
Lenstra AK, Shamir A (2000) Analysis and optimization of the TWINKLE factoringDevice.Proc Eurocrypt 2000. LNCS, vol 1807. Springer, pp 35–52
Madou MJ (2002) Fundamentals of Microfabrication: The Science ofMiniaturization, 2nd edn. CRC Press, Boca Raton
Plummer D, Dalton LJ, Peter F (1999) The recodable locking device. Commun ACM42(7):83–87
Wang H (1963) Dominoes and the AEA Case of the Decision Problem. In: J Fox(ed) Mathematical Theory of Automata. Polytechnic Press, Brooklyn, pp 23–55
Branko GS, Shepard GC (1987) Tilings and Patterns. H Freeman,Gordonsville. Chapter 11
Berger R (1966) The Undecidability of the Domino Problem. Mem Am Math Soc66:1–72
Lewis HR, Papadimitriou CH (1981) Elements of the Theory ofComputation. Prentice-Hall, Upper Saddle River, pp 296–300, 345–348
Winfree E (1998) Simulations of Computing by Self‐Assembly. In:Proceedings of the Fourth Annual Meeting on DNA Based Computers, held at the University of Pennsylvania. pp 16–19
Xia Y, Whitesides GM (1998) Soft Lithography. Annu Rev Mater Sci28:153–184
Rothemund PWK (2000) Using lateral capillary forces to compute byself‐assembly. Proc Nat Acad Sci (USA) 97:984–989
Seeman NC (2004) Nanotechnology and the Double Helix. Sci Am290(6):64–75
Reif JH, LaBean TH (2007) Nanostructures and Autonomous Devices Assembledfrom DNA In: Eshaghian-Wilner MM (ed) Nano‐scale and Bio‐inspired Computing. Wiley, Malden
Adleman LM (1994) Molecular computation of solutions to combinatorialproblems. Science 266(11):1021–1024
Adleman L (1998) Computing with DNA. Sci Am279(2):34–41
Winfree E, Liu F, Wenzler LA, Seeman NC (1998) Design andSelf‐Assembly of Two‐Dimensional DNA Crystals. Nature 394:539–544
Yan H, LaBean TH, Feng L, Reif JH (2003) Directed Nucleation Assembly ofBarcode Patterned DNA Lattices. PNAS 100(14):8103–8108
Rothemund PWK (2006) Folding DNA to create nanoscale shapes andpatterns. Nature 440:297–302
Mao C, LaBean TH, Reif JH, Seeman (2000) Logical Computation UsingAlgorithmic Self‐Assembly of DNA Triple‐Crossover Molecules. Nature 407:493–495
Yan H, Feng L, LaBean TH, Reif J (2003) DNA Nanotubes, Parallel MolecularComputations of Pairwise Exclusive-Or (XOR) Using DNA String Tile Self‐Assembly. J Am Chem Soc (JACS)125(47):14246–14247
Rothemund PWK, Papadakis N, Winfree E (2004) Algorithmic Self‐Assemblyof DNA Sierpinski Triangles. PLoS Biology 2(12), e424. doi:10.1371/journal.pbio.0020424
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
Reif JH, Sahu S (2008) Autonomous Programmable DNA Nanorobotic Devices UsingDNAzymes, John H. Reif and Sudher Sahu.In: Garzon M, Yan H (eds) Autonomous Programmable DNA Nanorobotic Devices Using DNAzymes, 13th InternationalMeeting on DNA Computing (DNA 13). Lecture Notes for Computer Science (LNCS). Springer, Berlin. To appear in special Journal Issue on Self-Assembly,Theoretical Computer Science (TCS)
Reif JH, LaBean TH (2007) Autonomous Programmable Biomolecular Devices UsingSelf‐Assembled DNA Nanostructures. Comm ACM (CACM) 50(9):46–53. Extended version:http://www.cs.duke.edu/~reif/paper/AutonomousDNA/AutonomousDNA.pdf
Bath J, Turberfield AJ (2007) DNA nanomachines. Nat Nanotechnol2:275–284
Acknowledgments
We sincerely thank Charles Bennett for his numerous suggestions and very important improvements to this survey. This work has been supportedby NSF grants CCF-0432038 and CCF-0523555.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag
About this entry
Cite this entry
Reif, J.H. (2012). Mechanical Computing: The Computational Complexity of Physical Devices. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_118
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1800-9_118
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1799-6
Online ISBN: 978-1-4614-1800-9
eBook Packages: Computer ScienceReference Module Computer Science and Engineering