Trancón y Widemann, B; Hauhs, M: Distributive-Law Semantics for Cellular Automata and Agent- Based Models, Lecture Notes in Computer Science, 6859, 344-358 (2011), doi:10.1007/978-3-642-22944-2_24
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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