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Distributive-Law Semantics for Cellular Automata and Agent-Based Models

  • Baltasar Trancón y Widemann
  • Michael Hauhs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6859)

Abstract

We present an effort to give formal semantics to the popular but theoretically rather unreflected scientific modelling paradigm of agent- or individual-based models. To this end, we give a generic formalization of two-dimensional cellular automata with flexible topology as the abstract basis of such models. The semantic approach of structural operational semantics a la Turi and Plotkin [7], based on bialgebras and distributive laws, leads in this case to a natural separation of the concerns of spatial structure, temporal behavior and local interaction. We give a generic distributive law for local behavior of automata and prove the equivalence to a more traditional, array-based formalization.

Keywords

Cellular Automaton Unique Homomorphism Programming Style Functional Programming Language Structural Operational Semantic 
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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Supplementary material

References

  1. 1.
    Bartels, F.: On Generalised Coinduction and Probabilistic Specification Formats. Phd thesis. Vrije Universiteit Amsterdam (2004)Google Scholar
  2. 2.
    Grimm, V., Berger, U., Bastiansen, F., Eliassen, S., Ginot, V., Giske, J., Goss-Custard, J., Grand, T., Heinz, S., Huse, G., Huth, A., Jepsen, J., Jørgensen, C., Mooij, W., Müller, B., Pe’er, G., Piou, C., Railsback, S., Robbins, A., Robbins, M., Rossmanith, E., Rüger, N., Strand, E., Souissi, S., Stillman, R., Vabø, R., Visser, U., DeAngelis, D.: A standard protocol for describing individual-based and agent-based models. Ecological Modelling 198, 115–126 (2006)CrossRefGoogle Scholar
  3. 3.
    Klin, B.: Structural operational semantics and modal logic, revisited. Electr. Notes Theor. Comput. Sci. 264(2), 155–175 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Kurth, W., Sloboda, B.: Growth grammars simulating trees. Silva Fennica 31, 285–295 (1997)Google Scholar
  5. 5.
    Kurz, A.: Logics for Coalgebras and Applications to Computer Science. Phd thesis. Ludwig-Maximilians-Universität München (2000)Google Scholar
  6. 6.
    Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Turi, D., Plotkin, G.: Towards a mathematical operational semantics. In: Proceedings 12th International Conference on Logic in Computer Science (LICS), pp. 280–291. IEEE, Los Alamitos (1997)Google Scholar
  8. 8.
    Tyler, T.: Cellular automata, http://cell-auto.com/neighbourhood/
  9. 9.
    Trancón y Widemann, B., Hauhs, M.: Distributive-law semantics for cellular automata and agent-based models (2011), https://www.bayceer.uni-bayreuth.de/mod/de/top/dl/96591/biabm-appendix-only.pdf (electronic appendix)

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Baltasar Trancón y Widemann
    • 1
  • Michael Hauhs
    • 1
  1. 1.Ecological ModellingUniversity of BayreuthGermany

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