Distributive-law semantics for cellular automata and agent-based models

Authors:
Baltasar Trancón y Widemann;Michael Hauhs
Affiliations:
Ecological Modelling, University of Bayreuth, Germany;Ecological Modelling, University of Bayreuth, Germany
Venue:
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Year:
2011

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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.