Mechanical Computation: The Computational Complexity of Physical Computing Devices Chapter, Encyclopedia of Complexity and Systems Science1 John H. Reif2 Article Outline Glossary I. Definition of the Subject and Its Importance II. Introduction to Computational Complexity III. Computational Complexity of Mechanical Devices and their Movement Problems IV. Concrete Mechanical Computing Devices V. Future Directions VI. Bibliography Glossary - 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: 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. 1 This is a revised and updated version of John H. Reif, Mechanical Computing: The Computational Complexity of Physical Devices, invited chapter, Encyclopedia of Complexity and System Science (edited by Andrew Spencer), Springer-Verlag, Heidelberg, Germany, (2013). Published online: http://www.springerreference.com/docs/html/chapterdbid/60497.html 2 Department of Computer Science, Duke University, Box 90129, Durham, NC 27708- 90129 USA. E-mail:
[email protected]. This work was supported by NSF grants NSF Grants CCF-1217457, CCF-1320360 and CCF-1617791. I. Definition of the Subject and Its Importance Mechanical devices for computation appear to be largely displaced by the widespread use of microprocessor-based computers that are pervading almost all aspects of our lives. Nevertheless, mechanical devices for computation are of interest for at least three reasons: (a) Historical: The use of mechanical devices for computation is of central importance in the historical study of technologies, with a history dating to thousands of years and with surprising applications even in relatively recent times.