Evolutionary information theory is a constructive approach that studies information in the context of evolutionary processes, which are ubiquitous in nature and society. In this paper, we develop foundations of evolutionary information theory, building several measures of evolutionary information and obtaining their properties. These measures are based on mathematical models of evolutionary computations, machines and automata. To measure evolutionary information in an invariant form, we construct and study universal evolutionary machines and automata, which form the base for evolutionary information theory. The first class of measures introduced and studied in this paper is evolutionary information size of symbolic objects relative to classes of automata or machines. In particular, it is proved that there is an invariant and optimal evolutionary information size relative to different classes of evolutionary machines. As a rule, different classes of algorithms or automata determine different information size for the same object. The more powerful classes of algorithms or automata decrease the information size of an object in comparison with the information size of an object relative to weaker4 classes of algorithms or machines. The second class of measures for evolutionary information in symbolic objects is studied by introduction of the quantity of evolutionary information about symbolic objects relative to a class of automata or machines. To give an example of applications, we briefly describe a possibility of modeling physical evolution with evolutionary machines to demonstrate applicability of evolutionary information theory to all material processes. At the end of the paper, directions for future research are suggested.
References
[1]
Garzon, M.H. Evolutionary computation and the processes of life: On the role of evolutionary models in computing. In Proceeding of Ubiquity Symposium, November 2012.
[2]
Burgin, M.; Eberbach, E. Universality for Turing machines, inductive Turing machines and evolutionary algorithms. Fundam. Inform. 2009, 91, 53–77.
[3]
Burgin, M.; Eberbach, E. On foundations of evolutionary computation: An evolutionary automata approach. In Handbook of Research on Artificial Immune Systems and Natural Computing: Applying Complex Adaptive Technologies; Mo, H., Ed.; IGI Global: Hershey, PA, USA, 2009; pp. 342–360.
[4]
Burgin, M.; Eberbach, E. Bounded and periodic evolutionary machines. In Proceeding of 2010 Congress on Evolutionary Computation (CEC′2010), Barcelona, Spain, 2010; pp. 1379–1386.
[5]
Chaitin, G.J. Algorithmic Information Theory; Cambridge University Press: Cambridge, UK, 1987.
[6]
Li, M.; Vitanyi, P. An Introduction to Kolmogorov Complexity and its Applications; Springer-Verlag: New York, NY, USA, 1997.
[7]
Burgin, M. Superrecursive Algorithms; Springer: New York, NY, USA, 2005.
[8]
Burgin, M. Theory of Information: Fundamentality, Diversity and Unification; World Scientific Publishing: Singapore, 2010.
[9]
Dodig-Crnkovic, G. Significance of models of computation from Turing model to natural computation. Minds Mach. 2011, 21, 301–322, doi:10.1007/s11023-011-9235-1.
[10]
Dodig-Crnkovic, G.; Müller, V. A dialogue concerning two world systems: Info-computational vs. mechanistic. In Information and Computation; Dodig-Crnkovic, G., Burgin, M., Eds.; World Scientific: Singapore, 2011; pp. 149–184.
[11]
Fredkin, E. Digital mechanics. Physica D 1990, 45, 254–270, doi:10.1016/0167-2789(90)90186-S.
[12]
Lloyd, S. A theory of quantum gravity based on quantum computation. Available online: http://arxiv.org/abs/quant-ph/0501135 (accessed on 12 March 2013).
[13]
Wolfram, S.A. New Kind of Science; Wolfram Media: Champaign, IL, USA, 2002.
[14]
Zuse, K. Rechnender Raum; Friedrich Vieweg & Sohn: Braunschweig, Germany, 1969.
[15]
Smolin, L. Three Roads to Quantum Gravity; Basic Books: New York, NY, USA, 2001.
[16]
Smolin, L. Atoms of space and time. Sci. Am. 2004, 15, 66–75, doi:10.1038/scientificamerican0104-66.
[17]
Rovelli, C. Quantum Gravity; Cambridge University Press: Cambridge, UK, 2004.
[18]
Burgin, M. Multiple computations and Kolmogorov complexity for such processes. Not. Acad. Sci. USSR 1983, 27, 793–797.
[19]
Burgin, M. Algorithmic complexity of recursive and inductive algorithms. Theor. Comput. Sci. 2004, 317, 31–60, doi:10.1016/j.tcs.2003.12.003.
[20]
Burgin, M. Measuring Power of Algorithms, Computer Programs, and Information Automata; Nova Science Publishers: New York, NY, USA, 2010.
[21]
Burks, A.; Wright, J. The theory of logical nets. Proc. Inst. Radio Eng. 1953, 41, 1357–1365.
[22]
Blum, L.; Cucker, F.; Shub, M.; Smale, S. Complexity and Real Computation; Springer-Verlag: New York, NY, USA, 1997.