Conservative logic

  • Edward Fredkin
  • Tommaso Toffoli
Article

Abstract

Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the conservation of certainadditive quantities (among which energy plays a distinguished role). Because it more closely mirrors physics than traditional models of computation, conservative logic is in a better position to provide indications concerning the realization of high-performance computing systems, i.e., of systems that make very efficient use of the “computing resources” actually offered by nature. In particular, conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation. After establishing a general framework, we discuss two specific models of computation. The first uses binary variables and is the conservative-logic counterpart of switching theory; this model proves that universal computing capabilities are compatible with the reversibility and conservation constraints. The second model, which is a refinement of the first, constitutes a substantial breakthrough in establishing a correspondence between computation and physics. In fact, this model is based on elastic collisions of identical “balls,” and thus is formally identical with the atomic model that underlies the (classical) kinetic theory of perfect gases. Quite literally, the functional behavior of a general-purpose digital computer can be reproduced by a perfect gas placed in a suitably shaped container and given appropriate initial conditions.

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References

  1. Baierlein, R. (1971).Atoms and Information Theory. W. H. Freeman. San Francisco.Google Scholar
  2. Bekenstein, J. D. (1981 a). “Universal upper bound to entropy-to-energy ratio for bounded systems,”Physiocal Review D,23, 287–298.Google Scholar
  3. Bekenstein, J. D. (1981b). “Encrgy cost of information transfer,”Physical Review Letters,46, 623–626.Google Scholar
  4. Benioff, P. (1980). “The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines,”Journal of Statistical Physics,22, 563–591.Google Scholar
  5. Bennett, C. H. (1973). “Logical reversibility of computation,”IBM Journal of Research and Development,6, 525–532.Google Scholar
  6. Bennett, C. H. (1979). “Dissipation-error tradeoff in proofreading.”BioSystems,11, 85–91.Google Scholar
  7. Feynman, R. (1963).Lectures on Physics, Vol. I. Addison-Wesley, Reading, Massachusetts.Google Scholar
  8. Fredkin, E., and Toffoli, T. (1978). “Design principles for achieving high-performance submicron digital technologies,” Proposal to DARPA, MIT Laboratory for Computer Science.Google Scholar
  9. Haken, H., (1975). “Cooperative phenomena,”Reviews of Modern Physics,47, 95.Google Scholar
  10. Herrell, D. J. (1974). “Femtojoule Josephson tunnelling logic gates,”IEEE Journal of Solid State Circuits.SC9, 277–282.Google Scholar
  11. Katz, A. (1967).Principles of Statistical Mechanics—The Information Theory Approach, Freeman, San Francisco.Google Scholar
  12. Keyes, R. W. (1977). “Physical uncertainty and information,”IEEE Transactions on Computers C26, 1017–1025.Google Scholar
  13. Kinoshita, K., Tsutomu, S., Jun, M. (1976). “On magnetic bubble circuits,”IEEE Transactions on Computers,C25, 247–253.Google Scholar
  14. Landau, L. D., and Lifshitz, E. M. (1960).Mechanics. Pergamon Press, New York.Google Scholar
  15. Landauer R. (1961). “Irreversibility and heat generation in the computing process,”IBM Journal of Research and Development,5, 183–191.Google Scholar
  16. Landauer, R. (1967). “Wanted: a physically possible theory of physics,”IEEE Spectrum,4, 105–109.Google Scholar
  17. Landauer, R. (1976). “Fundamental limitations in the computational process,”Berichte der Bunsengesellschaft fuer Physikalische Chemie,80, 1041–1256.Google Scholar
  18. Ohanian, H. C. (1976).Gravitation and Spacetime, Norton. New York.Google Scholar
  19. Petri, C. A. (1976). “Grundsätzliches zur Beischreibung diskreter Prozesse,” 3rd Colloquium über Automatentheorie, Basel, Birkhäuser Verlag. (An English translation is available from Petri or from the authors).Google Scholar
  20. Priese, L. (1976). “On a simple combinatorial structure sufficient for sublying nontrivial self-reproduction,”Journal of Cybernetics,6, 101–137.Google Scholar
  21. Ressler, A., The design of a conservative logic computer and a graphical editor simulator. M. S. Thesis. MIT, EECS Department (January 1981).Google Scholar
  22. Shannon, Claude E. “A mathematical theory of communication,”Bell Systems Technical Journal,27, 379–423 and 623–656.Google Scholar
  23. Toffoli, T. (1977). “Computation and construction universality of reversible cellular automata,”Journal of Computer Systems Science,15, 213–231.Google Scholar
  24. Toffoli, T. (1977). “Cellular automata mechanics,”Technical Report No. 208, Logic of Computers Group, CCS Department, The University of Michigan, Ann Arbor, Michigan (November).Google Scholar
  25. Toffoli, T. (1980). “Reversible computing,”Technical Memo MIT/LCS/TM-151, MIT Laboratory for Computer Science (February). An abridged version of this paper appeared under the same title inSeventh Colloquium on Automata, Languages and Programming, J. W. de Bakker and J. van Leeuwen, eds. Springer, Berlin (1980), pp. 632–644. An enlarged, revised version for final publication is in preparation.Google Scholar
  26. Toffoli, T. (1981). “Bicontinuous extensions of invertible combinatorial functions,”Mathematical Systems Theory,14, 13–23.Google Scholar
  27. Turing, A. M. (1936). “On computable numbers, with an application to the entscheidungs problem,”Proceedings of the London Mathematical Society Ser. 2 43, 544–546.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • Edward Fredkin
    • 1
  • Tommaso Toffoli
    • 1
  1. 1.MIT Laboratory for Computer ScienceCambridge

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