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DOI：http://dx.doi.org/10.26855/acc.2020.12.003

Physical world contains many complex sentient structures. They have evolved to learn how to organize themselves and optimally use the resources available to them while interacting with their environment. These complex adaptive systems (CAS) sustain their continued existence in the face of external forces causing large fluctuations. The study of CAS functions, structures and their dynamics under the influence of fluctuations has thrown light into self-organizing patterns that are common among these disparate systems. Common theme among these structures is that a system encodes and processes information to organize and manage its components interacting with each other and their environment. The self-organizing patterns also sense and counteract fluctuations to maintain their stability. They become autopoietic and maintain homeostasis. Digital Computing structures composed of distributed and communicating software and hardware components also fall into the category of a complex system where fluctuations in the demand for, or the availability of, resources required to execute the computa-tions disturb their stability and performance. The fluctuations impact the resilien-cy and efficiency of the structure as the scale of components increase. This paper describes the theory and practice of applying the self-organizing and self-managing patterns to distributed digital computing structures and making them autopoietic machines.

[1] Maturana, Humberto R. & Varela, Francisco J. (1980). Autopoiesis and Cognition. The Realization of the Living. Dordrecht: Reidel.

[2] Yang, A., & Shan, Y. (eds.) (2008). Intelligent Complex Adaptive Systems, IGI Publishing, Hershey, PA.

[3] Arthur, W. B., Durlauf, S., & Lane, D. (eds.) (1997). The Economy as an Evolving Complex System. Addison-Wesley, Reading, MA.

[4] Dooley, K. (1997). A complex adaptive systems model of organizational change. Non-linear Dynamics, Psychology and the Life Sciences, v. 1, pp. 69-97.

[5] Choi, Thomas Y., Kevin J. Dooley, & Manus Rungtusanatham. (2001). Supply Networks and Complex Adaptive Sysems: Control Versus Emergence. Journal of Operations Management, v. 19, No. 3, pp. 351-66.

[6] Miller, J., & Page, S. (2007). Complex adaptive Systems: An introduction to computational models of social life. Princeton, NJ: Princeton University Press.

[7] Mitchell, M. (2009). Complexity: a Guided Tour. Oxford: Oxford University Press.

[8] Beinhocker, E. D. (2006). The origins of wealth: evolution, complexity, and the radical remaking of economics. Boston: Harvard Business School Press.

[9] Beinhocker, E. D. (2010). Evolution as computation: Implications for economic theory and ontology. Santa Fe Working Paper 2010-12037. Santa Fe: Santa Fe Institute.

[10] Waldrop, W. Mitchell. (1992). Complexity: The Emerging Science at the Edge of Order and Chaos. New York: Touchstone.

[11] Burgin, M. (2011). Information in the structure of the world. International Journal Information Theories and Applications, v. 18, No. 1, pp. 16-32.

[12] Prigogine, I. Time, Structure and Fluctuations. Available online: https://www.nobelprize.org/uploads/2018/06/ prigogine-lecture.pdf (accessed on 16 June 2020).

[13] Prigogine, I., & Stengers, I. (1984). Order out of Chaos, Bantam Books, Toronto/New York/London.

[14] Burgin, Mark. (2017). The General Theory of Information as a Unifying Factor for Information Studies: The Noble Eight-Fold Path. Proceedings, v. 1, no. 3: 164.

[15] Frans de Waal. (2016). Are We Smart Enough to Know How Smart Animals are? W. W. Norton, New York.

[16] P. Cockshott, L. M. MacKenzie, & G. Michaelson. (2012). Computation and Its Limits, Oxford University Press, Oxford.

[17] R. Mikkilineni. (2012). Going beyond Computation and Its Limits: Injecting Cognition into Computing. Applied Mathematics, v. 3 No. 11A, pp. 1826-1835. doi: 10.4236/am.2012.331248.

[18] Burgin, M., & Adamatzky, A. (2017). Structural machines and slime mold computation. Int. J. Gen. Syst., v. 45, pp. 201-224.

[19] Burgin, M., & Adamatzky, A. (2017). Structural Machines as a Mathematical Model of Biological and Chemical Computers. Theory Appl. Math. Comput. Sci., v. 7, pp. 1-30.

[20] Burgin, M. (2020). Information Processing by Structural Machines, in Theoretical Information Studies: Information in the World, pp. 323-371.

[21] Burgin, M. (2017). Actors, Agents and Oracles in the Context of Artificial Intelligence. Journal of Artificial Intelli-gence Research & Advances, v. 4, No. 3, pp. 17-25.

[22] Rao Mikkilineni, Giovanni Morana., & Mark Burgin. (2015). Oracles in Software Networks: A New Scientific and Technological Approach to Designing Self-Managing Distributed Computing Processes, Proceedings of the 2015 European Conference on Software Architecture Workshops (ECSAW '15), 2015.

[23] Burgin, M. (2017). Inaccessible Information and the Mathematical Theory of Oracles, in Information Studies and the Quest for Transdisciplinarity: Unity through Diversity, World Scientific, New York/London/Singapore, pp. 59-114.

[24] Burgin, M. (2016). Theory of Knowledge: Structures and Processes. World Scientific Books: Singapore.

[25] Mikkilineni, R., & Burgin, M. (2020). Structural Machines as Unconventional Knowledge Processors. Proceedings, v. 47, 26.

[26] Burgin, M., & Mikkilineni, R. (2018). Cloud computing based on agent technology, super-recursive algorithms, and DNA. Int. J. Grid and Utility Computing, v. 9, No. 2, pp. 193-204.

[27] Turing, A. (1939). Systems of Logic Based on Ordinals, Proc. Lond. Math. Soc., Ser.2, v. 45, pp. 161-228.

[28] Shettleworth, S. J. (2001). Animal cognition and animal behaviour. Animal Behaviour, 61: 277-286.

[29] Turing, A. (1936). On Computable Numbers with an Application to the Entscheidungs-problem, Proc. Lond. Math. Soc., Ser. 2, v. 42, pp. 230-265.

[30] Von Neumann, J. (1949). Theory of Self-Reproducing Automata; University of Illinois Lectures on the Theory and Organization of Complicated Automata, Edited and completed by Arthur W. Burks; University of Illinois Press: Urbana, IL, USA.

[31] Burgin, M. (2005). Superrecursive Algorithms, Springer-Verlag, New York.

[32] Haykin, S. (1994). Neural Networks: A Comprehensive Foundation, New York, Macmillan.

[33] Kolmogorov, A. N. (1953). On the Concept of Algorithm, Russian Mathematical Surveys, v. 8, No. 4, pp. 175-176.

[34] Kleinberg, J., & Tardos, E. (2006). Algorithm Design, Pearson - Addison-Wesley.

[35] Goodrich, M. T., & Tamassia, R. (2015). Algorithm Design and Applications, Willey, Hoboken, NJ.

[36] Burgin, M. (2020). Triadic Automata and Machines as Information Transformers, Information, v. 11, No. 2, 102; doi: 10.3390/info11020102.

[37] Burgin, M. (2003). Nonlinear Phenomena in Spaces of Algorithms, International Journal of Computer Mathematics, v. 80, No. 12, pp. 1449-1476.

[38] Burgin, M. (2012). Structural Reality, Nova Science Publishers, New York.

[39] Robinson, A. (1963). Introduction to Model Theory and Metamathematics of Algebra, North-Holland, Amster-dam/New York.

[40] Yaglom, I. M. (1980). Mathematical Structures and Mathematical Modeling, Sov. Radio, Moscow (in Russian).

[41] Tegmark, M. (2008). The Mathematical Universe, Foundations of Physics, v. 38, No. 2, pp. 101-150.

[42] Bourbaki, N. (1957). Structures, Hermann, Paris.

[43] Bourbaki, N. (1960). Theorie des Ensembles, Hermann, Paris.

[44] C. Berge. (1973). Balanced hypergraphs and some applications to graph theory, in: J.N. Srivastava, ed., A Survey of Combinatorial Theory (North-Holland, Amsterdam, 1973) 15-23.

[45] Petri, C. A. (1962). Kommunikation mit Automaten. English Translation, 1966: Communication with Automata, Technical Report RADC-TR-65-377, Rome Air Dev. Center, New York.

[46] Burgin, M., & Eberbach, E. (2009). On foundations of evolutionary computation: an evolutionary automata ap-proach, in Hongwei Mo (Ed.), Handbook of Research on Artificial Immune Systems and Natural Computing: Ap-plying Complex Adaptive Technologies, IGI Global, Hershey, Pennsylvania, pp. 342-360.

[47] Burgin, M., & Bratalskii, E. (1986). The principle of asymptotic uniformity in complex system modelling, in Oper-ation Research and Automated Control Systems, Kiev: Institute of Cybernetics, pp. 115-122 [in Russian].

[48] Burgin, M., & Debnath, N. (2010). Reusability as Design of Second-Level Algorithms, in Proceedings of the ISCA 25th International Conference “Computers and their Applications” (CATA-2010), ISCA, Honolulu, Hawaii, 2010, pp. 147-152.

[49] Burgin, M., & Gupta, B. (2012). Second-level Algorithms, Superrecursivity, and Recovery Problem in Distributed Systems, Theory of Computing Systems, v. 50, No. 4, 2012, pp. 694-705.

[50] Burgin, M., Eberbach, E., & Mikkilineni, R. (2019). Cloud Computing and Cloud Automata as A New Paradigm for Computation. Computer Reviews Journal, v. 4, pp. 113-134. Retrieved from https://purkh.com/index.php /tocomp/article/view/459.

[51] R. Mikkilineni, & G. Morana. (2019). “Post-Turing Computing, Hierarchical Named Networks and a New Class of Edge Computing,” 2019 IEEE 28th International Conference on Enabling Technologies: Infrastructure for Colla-borative Enterprises (WETICE), Napoli, Italy, pp. 82-87, doi: 10.1109/WETICE.2019.00024.

[52] Mikkilineni, R., Comparini, A., & Morana, G. (2012). The Turing o-machine and the DIME Network Architecture: Injecting the Architectural Resiliency into Distributed Computing. Turing100, The Alan Turing Centenary, Easy-Chair Proceedings in Computing. 2012. Available online: https://easychair.org/publications/paper/gBD (accessed on 12 May 2020).

[53] W. Aspray, & A. Burks. (1989). Papers of John von Neumann on Computing and Computer Theory. MIT Press, Cambridge.

Autopoietic Computing Systems and Triadic Automata: The Theory and Practice

**How to cite this paper:** Mark Burgin, Rao Mikkilineni, Vidya Phalke. (2020) Autopoietic Computing Systems and Triadic Automata: The Theory and Practice. *Advances in Computer and Communication*, **1**(**1**), 16-35.

DOI: http://dx.doi.org/10.26855/acc.2020.12.003

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