Skip to main content

Identification of Cellular Automata

  • Living reference work entry
  • First Online:
Encyclopedia of Complexity and Systems Science

Glossary

Cellular automaton:

is an array of finite automata connected locally, which update their states in discrete time and at the same moments; every automaton updates its next state depending on the states of its closest neighbors.

Decision tree:

is a mapping from a classified set of observations about an event to the conclusion about its outcome.

Deterministic automaton :

has only one next state for each pair of internal and input states.

Finite automaton:

is an abstract machine which takes a finite number of states and transitions between the states; the machine changes its states depending on the input states.

Immunocomputing:

replicates principles of information processing by immune networks to perform computation.

Learning automaton:

modifies its transition rules depending on its past experience.

Learning classifier system:

is a rule-based system, a population of rules, which are processed, selected, and updated using reinforcement learning techniques.

Machine learning:
...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Bibliography

Primary Literature

  • Adamatzky A (1990) Identification of probabilistic cellular automata. Izv AN SSSR Ser Tekhnicheskaya Kibern 3:95–100 (in Russian). Translated in Soviet (1990) J Comput Syst Sci 30:118–123

    Google Scholar 

  • Adamatzky A (1991) Identification of fuzzy cellular automata. Autom Comput 6:75–80

    Google Scholar 

  • Adamatzky A (1992a) Complexity of cellular automata identification. Avtom Telemeh 9:72–86 (in Russian). Translated (1992) Complexity of identification of cellular automata. Autom Remote Control 53(9/2):1449–1458

    Google Scholar 

  • Adamatzky A (1992b) Identification of nonstationary cellular automata. J Comp Sci Tech 7:379–382

    Article  MathSciNet  MATH  Google Scholar 

  • Adamatzky A (1992c) On complexity of identification of nonstationary cellular automata. Izv AN SSSR Ser Tekhnicheskaya Kibern 3:74–79. (in Russian)

    Google Scholar 

  • Adamatzky A (1993a) Implantation of cellular automata. Appl Math Comput 55:49–71

    MathSciNet  MATH  Google Scholar 

  • Adamatzky A (1993b) Identification of distributed intelligence. Izv AN SSSR Ser Tekhnicheskaya Kibern 6:359–369 (in Russian). Translated (1995) Recognition of distributed intelligence. J Comp Syst Sci Int 33:160–169

    Google Scholar 

  • Adamatzky A (1994a) Hierarchy of fuzzy cellular automata. J Fuzzy Sets Syst 62:167–174

    Article  MathSciNet  Google Scholar 

  • Adamatzky A (1994b) On complexity of serial simulation of cellular-automata mappings. Avtom Telemeh 3 (in Russian). Translated (1994) Complexity of sequential realisation of cellular-automata maps. Autom Remote Control 55(2/2):271–280

    Google Scholar 

  • Adamatzky A (1994c) Identification of cellular automata. Taylor and Francis, London

    MATH  Google Scholar 

  • Adamatzky A (1997) Automatic programming of cellular automata: identification approach. Kybernetes 26:126–135

    Article  Google Scholar 

  • Adamatzky A, Bronnikov V (1989) Identification of additive cellular automata. Izv AN SSSR Ser Tekhnicheskaya Kibern 3:200–205 (in Russian). Translated in Soviet (1990) J Comput Syst Sci 28:47–51

    Google Scholar 

  • Adamatzky A, Tolmachiev D (1997) Chemical processor for computation of skeleton of planar shape. Adv Mater Opt Electron 7:535–539

    Google Scholar 

  • Andre D, Bennett FH III, Koza JR (1996) Discovery by genetic programming of a cellular automata rule that is better than any known rule for the majority classification problem. In: Koza JR (ed) Genetic programming 1996. Proceedings of the 1st annual conference. MIT Press, Cambridge

    Google Scholar 

  • Brauer W (1984) Automaton-theorie. Teubner BG, Stuttgart

    Google Scholar 

  • Bull L (2005) Two simple learning classifier systems. In: Bull L, Kovacs T (eds) Foundations of learning classifier systems. Springer, New York, pp 63–90

    Chapter  Google Scholar 

  • Bull L, Adamatzky A (2007) A learning classifier system approach to the identification of cellular automata. J Cell Autom 2(1):21–38

    MathSciNet  MATH  Google Scholar 

  • Bull L, Adamatzky A, De Lacy Costello B (2003) The automatic identification of spatially extended reaction-diffusion systems. EPSRC Proposal GR/S68798/01, University of the West of England

    Google Scholar 

  • Das R, Crutchfield J, Mitchell M, Hanson J (1995) Evolving globally synchronized cellular automata. In: Eshelman L (ed) Proc 6th Int Conf on genetic algorithms. Morgan Kaufmann, New York, pp 336–343

    Google Scholar 

  • El Yacoubi S, Jacewicz P (2007) A genetic programming approach to structural identification of cellular automata. J Cell Autom 2(1):67–76

    MathSciNet  MATH  Google Scholar 

  • Heijmans HJAM (1990) Iteration of morphological transformations. CWI Q 9:19–36

    MATH  Google Scholar 

  • Jacewicz P, El Yacoubi S (1999) A genetic programming approach to structural identification of cellular automata. In: Proc of 3th International Conference on Parallel Processing and Applied Mathematics, Kazimierz Dolny, Poland, 1999, pp 148–157

    Google Scholar 

  • Kleene SC (1956) Representation of events in nerve nets. In: Shannon CE, McCarthy J (eds) Automata Studies. Princeton University Press, Princeton, pp 3–41

    Google Scholar 

  • Koza JR (1994) Genetic programming II: automatic discovery of reusable programs. MIT Press, Cambridge

    MATH  Google Scholar 

  • Koza J, Bennett FH III, Andre D, Keane M (1999) Genetic programming III: Darwinian invention and problem solving. Morgan Kaufmann, New York

    MATH  Google Scholar 

  • Kudrjavtzev VB, Podkolzin AS, Bolotov AA (1990) The foundations of the theory of homogeneous structures. Nauka Publishers, Moscow

    Google Scholar 

  • Maeda K, Sakama C (2003) Discovery of cellular automata rules using cases. In: Proceedings of the 6th international conference on discovery science, Lecture notes in artificial intelligence, vol 2843. Springer, Heidelberg, pp 357–364

    Google Scholar 

  • Maeda K, Sakama C (2007) Identifying cellular automata rules. J Cell Autom 2:1–20

    MathSciNet  MATH  Google Scholar 

  • Mitchell M, Hraber PT, Crutchfield JP (1993) Revisiting the edge of chaos: evolving cellular automata to perform computations. Complex Syst 7:89–130

    MATH  Google Scholar 

  • Mitchell M, Crutchfield J, Hraber P (1994) Evolving cellular automata to perform computations: mechanisms and impediments. Phys D 75:361–391

    Article  MATH  Google Scholar 

  • Moore EF (1956) Gedanken-experiments on sequential machines. In: Shannon CE, McCarthy J (eds) Automata studies. Princeton University Press, Princeton, pp 129–153

    Google Scholar 

  • Murphy KP (1996) Passively learning finite automata. Technical Report 96-04-017, Santa-Fe Institute, Santa Fe

    Google Scholar 

  • Ronse C (1985) Definition of convexity and convex hulls in digital images. Bull Soc Math Belg Ser B 37:71–85

    MathSciNet  MATH  Google Scholar 

  • Tarakanov A, Prokaev A (2007) Identification of cellular automata by immunocomputing. J Cell Autom 2(1):39–45

    MathSciNet  MATH  Google Scholar 

  • Tarakanov A, Skormin V, Sokolova S (2003) Immunocomputing: principles and applications. Springer, New York

    Book  MATH  Google Scholar 

  • Tolmachiev D, Adamatzky A (1996) Chemical processor for computation of Voronoi diagram. Adv Mater Opt Electron 6:191–196

    Article  Google Scholar 

  • Trakhtenbrot BA (1957) On operators, realizable in logical nets. DAN SSSR. Proceedings of the USSR Academy of Sciences 112:1005–1007. (in Russian)

    Google Scholar 

  • Trakhtenbrot BA, Bardzin YAM (1970) Finite automata (behaviour and synthesis). Nauka Publishers, Moscow

    Google Scholar 

  • Von Neumann J (1990) Theory of self-reproducing automata. University of Illinois, Urbana

    Google Scholar 

  • Voorhees B (1996) Computational analysis of one-dimensional cellular automata. World Scientific, Singapore

    MATH  Google Scholar 

  • Wolfram S (1994) Cellular automata and complexity: collected papers. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Wuensche A, Lesser M (1992) The global dynamics of cellular automata. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Yang YX, Billings SA (2003a) Identification of probabilistic cellular automata. IEEE Trans Syst Man Cybern B 33:225–236

    Google Scholar 

  • Yang YX, Billings SA (2003b) Identification of the neighbourhood and CA rules from spatio-temporal CA patterns. IEEE Trans Syst Man Cybern B 30:332–339

    Google Scholar 

  • Zhao Y, Billings SA (2006) Neighborhood detection using mutual information for the identification of cellular automata. IEEE Trans Syst Man Cybern B 36:473–479

    Article  Google Scholar 

  • Zhao Y, Billings SA (2007) The identification of cellular automata. J Cell Autom 2(1):21–38

    MathSciNet  MATH  Google Scholar 

  • Zhao Y, Billings SA, Routh A (2005) Identification of excitable media using cellular automata. Int J Bifur Chaos 17:153–168

    Article  MATH  Google Scholar 

Additional Reading

  • Adamatzky A (2001) Computation in nonlinear media and automata collectives. IoP Publishing, Bristol

    Book  MATH  Google Scholar 

  • Brauer W (1984) Automaton-theorie. Teubner, London

    Google Scholar 

  • Chopard B, Droz M (1998) Cellular automata modeling of physical systems. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Crutchfield JP, Hanson JE (1999) Computational mechanics of cellular processes. Princeton University Press, Princeton

    Google Scholar 

  • Narendra K, Thathachar MAL (1989) Learning automata. Prentice-Hall, Upper Saddle River

    MATH  Google Scholar 

  • Prokaev A, Sokolova L, Tarakanov A (2007) Using immunocomputing to forecast hydrophysical fields in the ocean. In: Int Workshop on Information Fusion and GIS (IF GIS 07), St. Petersburg (accepted for publication in LNCS)

    Google Scholar 

  • Sipper M (1997) Evolution of parallel cellular machines. In: The cellular programming approach, Lecture notes in computer science, vol 1194. Springer, Berlin

    Google Scholar 

  • Tarakanov A, Adamatzky A (2002) Virtual clothing in hybrid cellular automata. Kybernetes (Int J Syst Cybernetics) 31:394–405

    MATH  Google Scholar 

  • Tarakanov A, Goncharova L, Tarakanov O (2005) A cytokine formal immune network, Lecture Notes in Artificial Intelligence, vol 3630, pp 510–519

    Google Scholar 

  • Tarakanov A, Prokaev A, Varnaskikh E (2007) Immunocomputing of hydroacoustic fields. Int J Unconv Comput 3:123–133

    Google Scholar 

  • Tarakanov A, Skormin V, Sokolova S (2003) Immunocomputing: principles and applications. Springer, New York

    Book  MATH  Google Scholar 

  • Toffoli T, Margolus N (1987) Cellular automata machines. A new environment for modeling, MIT press series in scientific computation. MIT Press, Cambridge

    MATH  Google Scholar 

  • Weimar J (1998) Simulation with cellular automata. Logos, Berlin

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrew Adamatzky .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media LLC

About this entry

Cite this entry

Adamatzky, A. (2017). Identification of Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_280-6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27737-5_280-6

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27737-5

  • Online ISBN: 978-3-642-27737-5

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

Publish with us

Policies and ethics