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.
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References
Bartels, F.: On Generalised Coinduction and Probabilistic Specification Formats. Phd thesis. Vrije Universiteit Amsterdam (2004)
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)
Klin, B.: Structural operational semantics and modal logic, revisited. Electr. Notes Theor. Comput. Sci. 264(2), 155–175 (2010)
Kurth, W., Sloboda, B.: Growth grammars simulating trees. Silva Fennica 31, 285–295 (1997)
Kurz, A.: Logics for Coalgebras and Applications to Computer Science. Phd thesis. Ludwig-Maximilians-Universität München (2000)
Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000)
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)
Tyler, T.: Cellular automata, http://cell-auto.com/neighbourhood/
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)
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Appendix containing omitted proofs and advanced examples. (276KB)
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Trancón y Widemann, B., Hauhs, M. (2011). Distributive-Law Semantics for Cellular Automata and Agent-Based Models. In: Corradini, A., Klin, B., Cîrstea, C. (eds) Algebra and Coalgebra in Computer Science. CALCO 2011. Lecture Notes in Computer Science, vol 6859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22944-2_24
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DOI: https://doi.org/10.1007/978-3-642-22944-2_24
Publisher Name: Springer, Berlin, Heidelberg
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