Recursively Generated Evolutionary Turing Machines and Evolutionary Automata

  • Mark Burgin
  • Eugene Eberbach
Part of the Studies in Computational Intelligence book series (SCI, volume 427)

Abstract

One of the roots of evolutionary computation was the idea of Turing about unorganized machines. The goal of this paper is the development of foundations for evolutionary computations, connecting Turing’s ideas and the contemporary state of art in evolutionary computations. The theory of computation is based on mathematical models of computing automata, such as Turing machines or finite automata. In a similar way, the theory of evolutionary computation is based on mathematical models of evolutionary computing automata, such as evolutionary Turing machines or evolutionary finite automata. The goal of the chapter is to study computability in the context of the theory of evolutionary computation and genetic algorithms. We use basic models of evolutionary computation, such as different types of evolutionary machines, evolutionary automata and evolutionary algorithms, for exploration of the computing and accepting power of various kinds of evolutionary automata. However, we consider not only how evolutionary automata compute but also how they are generated because a rigorous study of construction techniques for computational systems is an urgent demand of information processing technology. Generation schemas for evolutionary automata are studied and applied to computability problems.

Keywords

Evolutionary Algorithm Fitness Function Evolutionary Computation Turing Machine Finite Automaton 
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.

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References

  1. Arya, S., Malamatos, T., Mount, D.M.: A simple entropy-based algorithm for planar point location. In: Proc. 12th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 262–268 (2001)Google Scholar
  2. Back, T., Fogel, D.B., Michalewicz, Z. (eds.): Handbook of Evolutionary Computation. Oxford University Press, Oxford (1997)Google Scholar
  3. Banks, E.: Information Processing and Transmission in Cellular Automata. PhD thesis. MIT, Department of Mechanical Engineering (1971)Google Scholar
  4. Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press (1999)Google Scholar
  5. Box, G.E.P.: Evolutionary operation: A method for increasing industrial productivity. Appl. Statistics VI, 81–101 (1957)CrossRefGoogle Scholar
  6. Burgin, M.: Multiple computations and Kolmogorov complexity for such processes. Notices of the Academy of Sciences of the USSR 27(2), (269(4)), 793–797 (1983) (translated from Russian) Google Scholar
  7. Burgin, M.: Reflexive Calculi and Logic of Expert Systems. In: Creative Processes Modeling by Means of Knowledge Bases, Sofia, pp. 139–160 (1992)Google Scholar
  8. Burgin, M.: Universal limit Turing machines. Notices of the Russian Academy of Sciences 325(4), 654–658 (1993) (translated from Russian 46(1), 79-83 (1993))MathSciNetGoogle Scholar
  9. Burgin, M.: Super-recursive Algorithms as a Tool for High Performance Computing. In: Proc. of the High Performance Computing Symposium, San Diego, pp. 224–228 (1999)Google Scholar
  10. Burgin, M.: Nonlinear Phenomena in Spaces of Algorithms. International Journal of Computer Mathematics 80(12), 1449–1476 (2003)MathSciNetMATHCrossRefGoogle Scholar
  11. Burgin, M.: From Neural networks to Grid Automata. In: Proceedings of the IASTED International Conference ”Modeling and Simulation”, pp. 307–312. Palm Springs, California (2003a)Google Scholar
  12. Burgin, M.: Cluster Computers and Grid Automata. In: Proceedings of the ISCA 17th International Conference “Computers and their Applications”. International Society for Computers and their Applications, Honolulu, Hawaii, pp. 106–109 (2003b)Google Scholar
  13. Burgin, M.: Superrecursive Algorithms. Springer, New York (2005)Google Scholar
  14. Burgin, M.: Measuring Power of Algorithms, Computer Programs, and Information Automata. Nova Science Publishers, New York (2010)Google Scholar
  15. Burgin, M., Eberbach, E.: Cooperative Combinatorial Optimization: Evolutionary Computation Case Study. BioSystems 91(1), 34–50 (2008)MathSciNetCrossRefGoogle Scholar
  16. Burgin, M., Eberbach, E.: Universality for Turing Machines, Inductive Turing Machines and Evolutionary Algorithms. Fundamenta Informaticae 91(1), 53–77 (2009)MathSciNetMATHGoogle Scholar
  17. Burgin, M., Eberbach, E.: On Foundations of Evolutionary Computation: An Evolutionary Automata Approach. In: Mo, H. (ed.) Handbook of Research on Artificial Immune Systems and Natural Computing: Applying Complex Adaptive Technologies, pp. 342–360. IGI Global, Hershey (2009a)CrossRefGoogle Scholar
  18. Burgin, M., Eberbach, E.: Bounded and Periodic Evolutionary Machines. In: Proc. 2010 Congress on Evolutionary Computation (CEC 2010), Barcelona, Spain, pp. 1379–1386 (2010)Google Scholar
  19. Casselman, S., Thornburg, M., Schewel, J.: Hardware Object Programming on the EVC1 - a Reconfigurable Computer. In: FPGAs for Rapid Board Development & Reconfigurable Computing (Photonics East 1995) (1995)Google Scholar
  20. Chow, H.A., Alnuweiri, H., Casselman, S.: FPGA-Based Transformable Computers for Fast Digital Signal Processing. In: 3rd Canadian Workshop on Field-Programmable Devices (FPD 1995), pp. 25–31 (1995)Google Scholar
  21. Codd, E.F.: Cellular Automata. Academic Press, New York (1968)MATHGoogle Scholar
  22. Dorigo, M., Colombetti, M.: Robot Shaping: An Experiment in Behavior Engineering. MIT Press, Cambridge (1997)Google Scholar
  23. Dorigo, M., Stuetzle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)MATHCrossRefGoogle Scholar
  24. Dozier, G.: Evolving robot behavior via interactive evolutionary computation: from real-world to simulation. In: Proceedings of the 2001 ACM Symposium on Applied Computing, Las Vegas, Nevada, pp. 340–344 (2001)Google Scholar
  25. Eberbach, E.: Neural Networks and Adaptive Expert Systems in the CSA Approach. Intern. Journal of Intelligent Systems, Special Issue on Artificial Neural Networks 8(4), 569–602 (1993)MATHGoogle Scholar
  26. Eberbach, E.: SEMAL: A Cost Language Based on the Calculus of Self-modifiable Algorithms. Intern. Journal of Software Engineering and Knowledge Engineering 4(3), 391–408 (1994)CrossRefGoogle Scholar
  27. Eberbach, E., Goldin, D., Wegner, P.: Turing’s Ideas and Models of Computation. In: Teuscher, C. (ed.) Alan Turing: Life and Legacy of a Great Thinker, pp. 159–194. Springer (2004)Google Scholar
  28. Eberbach, E.: Toward a theory of evolutionary computation. BioSystems 82, 1–19 (2005)CrossRefGoogle Scholar
  29. Eberbach, E., Burgin, M.: Evolution of Evolution: Self-constructing Evolutionary Turing Machine Case Study. In: Proc. 2007 Congress on Evolutionary Computation, CEC 2007, Singapore, pp. 4599–4604 (2007)Google Scholar
  30. Eberbach, E., Burgin, M.: Theoretical Framework for Cooperation and Competition in Evolutionary Computation. In: Proc. 2nd Intern. Conf. on Software and Data Technologies, ICSOFT 2007, Barcelona, Spain, July 22-25, vol. PL/DPS/KE/MUSE, pp. 229–234 (2007a)Google Scholar
  31. Eberbach, E., Burgin, M.: Evolutionary Automata as Foundation of Evolutionary Computation: Larry Fogel Was Right. In: Proc. 2009 Congress on Evolutionary Computation, CEC 2009, Trondheim, pp. 2149–2156 (2009)Google Scholar
  32. Estrin, G.: Organization of Computer Systems-The Fixed Plus Variable Structure Computer. In: Proc. Western Joint Computer Conf., Western Joint Computer Conference, New York, pp. 33–40 (1960)Google Scholar
  33. Fogel, D.B.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. IEEE Press (1995)Google Scholar
  34. Fogel, D.B.: An Introduction to Evolutionary Computation. In: Tutorial, Congress on Evolutionary Computation (CEC 2001), Seoul, Korea (2001)Google Scholar
  35. Fogel, L.J., Owens, A.J., Walsh, M.J.: Artificial Intelligence Through Simulated Evolutions. John Wiley, New York (1966)Google Scholar
  36. Fraser, A.S.: Simulation of genetic systems by automatic digital computers. Australian Journal of Biological Sciences 10, 484–491 (1957)Google Scholar
  37. Freund, R.: Real functions and numbers defined by Turing machines. Theoretical Computer Science 23(3), 287–304 (1983)MathSciNetMATHCrossRefGoogle Scholar
  38. Friedberg, R.M.: A learning machine. IBM J. 2, 2–13 (1958)MathSciNetCrossRefGoogle Scholar
  39. Friedberg, R.M., Dunham, B., North, J.H.: A learning machine: Part II. IBM J. 3, 282–287 (1959)MathSciNetCrossRefGoogle Scholar
  40. Friedman, G.J.: Selective feedback computers for engineering synthesis and nervous system analogy. Master’s thesis, UCLA (1956)Google Scholar
  41. Hartenstein, R.: A decade of reconfigurable computing: a visionary retrospective. In: Nebel, W., Jerraya, A. (eds.) Proceedings of the Conference on Design, Automation and Test in Europe (DATE 2001), Munich, Germany, pp. 642–649. IEEE Press, Piscataway (2001)CrossRefGoogle Scholar
  42. Hauck, S., DeHon, A.: Reconfigurable Computing: The Theory and Practice of FPGA-Based Computing. Morgan Kaufman (2008)Google Scholar
  43. He, J., Yao, X.: A study of drift analysis for estimating computation time of evolutionary algorithms. Nat. Comput. 3, 21–25 (2004)MathSciNetMATHCrossRefGoogle Scholar
  44. Holland, J.H.: Adapatation in Natural and Artificial Systems, 2nd edn. Univ. of Michigan Press, MIT Press, Ann Arbor (1975)Google Scholar
  45. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison Wesley, Boston (2001)MATHGoogle Scholar
  46. Ito, T., Ono, K., Ichikawa, M., Okuyama, Y., Kuroda, K.: Reconfigurable Instruction-Level Parallel Processor Architecture. In: Omondi, A.R., Sedukhin, S.G. (eds.) ACSAC 2003. LNCS, vol. 2823, pp. 208–220. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  47. JiJi, R.D., Andersson, G.G., Booksh, K.S.: Application of PARAFAC for calibration with excitation–emission matrix fluorescence spectra of three classes of environmental pollutants. J. Chemometrics 14, 171–185 (2000)CrossRefGoogle Scholar
  48. Katagami, D., Yamada, S.: Interactive Evolutionary Computation for Real Robot from Viewpoint of Observation. Joho Shori Gakkai Kenkyu Hokoku (97), 19–24 (2001)Google Scholar
  49. Kennedy, J., Eberhart, R.: Particle Swarm Optimization. In: Proc. of the 1995 IEEE Int. Conf. on Neral Networks, pp. 1942–1948 (1995)Google Scholar
  50. Kennedy, J., Eberhart, R., Shi, Y.: Swarm Intelligence. Morgan Kaufmann (2001)Google Scholar
  51. Kleene, S.C.: Mathematical logic: constructive and non-constructive operations. In: Proceedings of the International Congress of Mathematicians, 1958, pp. 137–153. Cambridge University Press, New York (1960)Google Scholar
  52. Koza, J.: Genetic Programming I, II, III. MIT Press (1992, 1994, 1999)Google Scholar
  53. Langton, C.G.: Self-Reproduction in Cellular Automata. Physica D: Nonlinear Phenomena 10(1-2), 135–144 (1984)CrossRefGoogle Scholar
  54. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. Springer (1996)Google Scholar
  55. Michalewicz, Z., Fogel, D.B.: How to Solve It: Moderrn Heuristics, 2nd edn. Springer (2004)Google Scholar
  56. Mo, H. (ed.): Handbook of Research on Artificial Immune Systems and Natural Computing: Applying Complex Adaptive Technologies. IGI Global, Hershey (2009)Google Scholar
  57. Nolfi, S., Floreano, D., Miglino, O., Mondada, F.: How to Evolve Autonomous Robots: Different Approaches in Evolutionary Robotics. In: Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems (Artificial Life IV), pp. 190–197 (1994)Google Scholar
  58. Rechenberg, I.: Evolutionstrategie: Optimierung technischer Systeme nach Prinizipien der biologischen Evolution. Fromman-Holzboog Verlag, Stuttgart (1973)Google Scholar
  59. Rice, H.G.: Recursive Real Numbers. In: Proceedings of the AMS, vol. 5, pp. 784–791 (1951)Google Scholar
  60. Rudolph, G.: Convergence analysis of canonical genetic algorithms. IEEE Trans. Neural Networks: Special Issue on EC 5(1), 96–101 (1994)Google Scholar
  61. Teuscher, C.: Turing’s Connectionism: An Investigation of Neural Network Architectures. Springer-Verlag (2002)Google Scholar
  62. Thornburg, M., Casselman, S.: Transformable Computers. In: International Parallel Processing Symposium (IPPS 1994), pp. 674–679 (1994)Google Scholar
  63. Trakhtenbrot, B.A., Barzdin, J.M.: Finite automata: behavior and synthesis. North-Holland, Amsterdam (1973)MATHGoogle Scholar
  64. Turing, A.: Intelligent Machinery. In: Collected Works of A.M. Turing: Mechanical Intelligence. Elsevier Science (1992)Google Scholar
  65. von Neumann, J.: The general and logical theory of automata. In: Cerebral Mechanisms in Behavior, The Hixon Symposium, pp. 1–31. Willey, New York (1951)Google Scholar
  66. von Neumann, J.: Theory of Self-Reproducing Automata. In: Burks, A.W. (ed.) 1949 University of Illinois Lectures on the Theory and Organization of Complicated Automata. University of Illinois Press, Urbana (1966)Google Scholar
  67. Wiedermann, J.: Characterizing the super-Turing computing power and efficiency of classical fuzzy Turing machines. Theoretical Computer Science 317(1-3), 61–69 (2004)MathSciNetMATHCrossRefGoogle Scholar
  68. Wolpert, D.H., Macready, W.G.: No free lunch theorem for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)CrossRefGoogle Scholar
  69. Yao, X.: Evolving artificial neural networks. Proceedings of the IEEE 87(9), 1423–1447 (1999)CrossRefGoogle Scholar
  70. Zadeh, L.A.: Fuzzy algorithms. Information and Control 12, 94–102 (1968)MathSciNetMATHCrossRefGoogle Scholar
  71. Chi, Z., Yan, H., Pham, T.: Fuzzy Algorithms: With Applications to Image Processing and Pattern Recognition. In: Advances in Fuzzy Systems - Applications and Theory, vol. 10 (1996)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2013

Authors and Affiliations

  • Mark Burgin
    • 1
  • Eugene Eberbach
    • 2
  1. 1.Dept. of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Dept. of Eng. and ScienceRensselaer Polytechnic InstituteHartfordUSA

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