Abstract
A new computing machine, called an active element machine (AEM), and the AEM programming language are presented. This computing model is motivated by the positive aspects of dendritic integration, inspired by biology, and traditional programming languages based on the register machine. Distinct from the traditional register machine, the fundamental computing elements . active elements . compute simultaneously. Distinct from traditional programming languages, all active element commands have an explicit reference to time. These attributes make the AEM an inherently parallel machine, enable the AEM to change its architecture (program) as it is executing its program. Using a random bit source from the environment and the Meta command, we show how to generate an AEM that represents an arbitrary real number in [0,1]. Exploiting the randomness from the environment, this example is extended to an AEM that can recognize an arbitrary binary language Lāāā{0,1}*. Finally, we demonstrate an AEM that finds the Ramsey number r(3,3), illustrating how parallel AEM algorithms and time in the commands help compute an NP-hard problem.
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References
Abelson, H., Sussman, G.J.: Structure and Interpretation of Computer Programs. MIT Press, Cambridge (1996)
Agnew, G.B.: Random sources for cryptographic systems. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol.Ā 304, pp. 77ā81. Springer, Heidelberg (1988)
Ajtai, M., KomlĆ³s, J., SzemerĆ©di, E.: A note on Ramsey numbers. Journal Combinatorial TheoryĀ 29(3), 354ā360 (1980)
Ajtai, M., KomlĆ³s, J., SzemerĆ©di, E.: A dense infinite Sidon sequence. European J. Combin.Ā 2(1), 1ā11 (1981)
Ajtai, M., KomlĆ³s, J., SzemerĆ©di, E.: Sorting in c logn parallel steps. CombinatoricaĀ 3(1), 1ā19 (1983)
Alon, N.: Eigenvalues, geometric expanders, sorting in rounds, and Ramsey theory. CombinatoricaĀ 6(3), 207ā219 (1986)
Alon, N.: Explicit Ramsey graphs and orthonormal labelings. Electron. J. Combin. Research Paper 12Ā 1, 8 (1994) (electronic)
Alon, N.: The Shannon capacity of a union. CombinatoricaĀ 18(3), 301ā310 (1998)
Axelrod, R., Hamilton, W.D.: The Evolution of Cooperation. Science New SeriesĀ 211(4489), 1390ā1396 (1981)
Burr, S.A.: Determining Generalized Ramsey Numbers is NP-hard. Ars CombinatoriaĀ 17, 21ā25 (1984)
Calude, C.S., Dinneen, M.J., Dumitrescu, M., Svozil, K.: Experimental Evidence of Quantum Randomness Incomputability. Phys. Rev. AĀ 82, 022102, 1ā8 (2010)
Cook, S.A.: The complexity of theorem proving procedures. In: Proceedings, Third Annual ACM Symposium on the Theory of Computing, pp. 151ā158. ACM, New York (1971)
Davis, M.: Computability and Unsolvability. Dover Publications, New York (1982)
Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39ā43 (1995)
Erdƶs, P., Szekeres, G.: A combinatorial problem in geometry. Compositio Math.Ā 2, 464ā470 (1935)
Erdƶs, P., Rado, R.: Combinatorial theorems on classifications of subsets of a given set. Proc. London Math.Ā 3(2), 417ā439 (1952)
Fiske, M.S.: Machine Learning. US 7,249,116 B2 (2003), http://tinyurl.com/3pcgfvr , or http://tinyurl.com/3pcgfvr
Fiske, M.S.: Effector Machine Computation. US 7,398,260 B2 (2004), Provisional 60/456,715 (2003), http://tinyurl.com/6l5wuhz or http://tinyurl.com/6l5wuhz
Fiske, M.S.: Active Element Machine Computation. US Application 20070288668 (2007), http://tinyurl.com/62gv8ke or http://tinyurl.com/62gv8ke
Furstenberg, H.: Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton (1981)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman (1979)
Graham, R.L., Rodl, V.: Numbers in Ramsey Theory. Surveys in Combinatorics. LMS Lecture Note Series 123. Cambridge University Press (1987)
Graham, R.L., Rothschild, B.L.: A Survey of Finite Ramsey Theorems. In: Proc. 2nd Louisiana State Univ. Conference on Combinatorics, Graph Theory and Computation, pp. 21ā40 (1971)
Hales, A.W., Jewett, R.I.: Regularity and positional games. Trans. Amer. Math. Soc.Ā 106, 222ā229 (1963)
Hertz, J., Krogh, A., Palmer, R.G.: Introduction To The Theory of Neural Computation. Addison-Wesley Publishing Company, California (1991)
Holland, J.H.: Outline for a logical theory of adaptive systems. JACMĀ 3, 297ā314 (1962)
Holland, J.H.: Adaptation in Natural and Artificial Systems. MIT Press, Cambridge (1992)
Quantique, I.D., Quantis, S.: Random Number Generation Using Quantum Optics (electronic), Geneva, Switzerland (2001-2011), http://www.idquantique.com/images/stories/PDF/quantis-random-generator/quantis-whitepaper.pdf
Koza, J.R.: Genetic Programming: On the Programming of Computer by Means of Natural Selection. MIT Press, Cambridge (1992)
Lee, E.A.: Computing Needs Time. Technical Report No. UCB/EECS-2009-30 (electronic). Electrical Engineering and Computer Sciences, University of California at Berkeley (2009), http://www.eecs.berkeley.edu/Pubs/TechRpts/2009/EECS-2009-30.html
McCulloch, W.S.: Walter Pitts. A logical calculus immanent in nervous activity. Bulletin of Mathematical BiophysicsĀ 5, 115ā133 (1943)
McKay, B.D., Radziszowski, S.P.: Subgraph counting identities and Ramsey numbers. Journal Combinatorial TheoryĀ 69(2), 193ā209 (1997)
Minsky, M.: Computation: Finite and Infinite Machines, 1st edn. Prentice-Hall, Inc., Englewood Cliffs (1967)
Paris, J., Harrington, L.: A mathematical incompleteness in Peano arithmetic. In: Barwise, J. (ed.) Handbook for Mathematical Logic. North-Holland (1977)
Rall, W.: The Theoretical Foundation of Dendritic Function. In: Segev, I., Rinzel, J., Shepherd, G. (eds.) Selected Papers of Wilfrid Rall with Commentaries. MIT Press, Cambridge (1995)
Ramsey, F.P.: On a problem of formal logic. Proc. London Math. Soc. SeriesĀ 2(30), 264ā286 (1930)
Roberts, F.S.: Applications of Ramsey theory. Discrete Appl. Math.Ā 9(3), 251ā261 (1984)
Robinson, A.: Non-standard Analysis. Princeton University Press, Princeton (1996), Revised Edition
Rothschild, B.L.: A generalization of Ramseyās theorem and a conjecture of Erdƶs. Doctoral Dissertation. Yale University, New Haven, Connecticut (1967)
Schur, I.: Uber die Kongruenz xmā+āymāā”āzm ( mod p). Deutsche Math.Ā 25, 114ā117 (1916)
Shannon, C.E.: The zero error capacity of a noisy channel. Transactions on Information Theory Institute of Radio EngineersĀ IT-2, 8ā19 (1956)
Spencer, J.H.: Ten Lectures on the Probabilistic Method, p. 4. SIAM (1994)
Stefanov, A., Gisin, N., Guinnard, O., Guinnard, L., Zbinden, H.: Optical quantum random number generator. Journal of Modern OpticsĀ 10, 1362ā3044 (2000)
Sturgis, H.E., Shepherdson, J.C.: Computability of Recursive Functions. J. Assoc. Comput. Mach.Ā 10, 217ā255 (1963)
Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc. SeriesĀ 2(42) (Parts 3 and 4), 230ā265 (1936); A correction, ibid. 43, 544ā546 (1937)
Yao, A.C.C.: Should tables be sorted? J. Assoc. Comput. Mach.Ā 28(3), 615ā628 (1981)
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Fiske, M.S. (2012). The Active Element Machine. In: Unger, H., Kyamaky, K., Kacprzyk, J. (eds) Autonomous Systems: Developments and Trends. Studies in Computational Intelligence, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24806-1_7
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