A Composable Discrete-Time Cellular Automaton Formalism

1. A Composable Discrete-TimeCellular Automaton Formalism Gary R. Mayer Hessam S. Sarjoughian Gary.Mayer@asu.edu Sarjoughian@asu.edu Arizona Center for Integrative Modeling & Simulation SBP ’08 01 April 2008 Phoenix, Arizona

2. Rationale • Cellular Automata has a central role in simulating many physical systems such as landscape processes • Interesting complex systems can be best described using CA and other kinds of models • Example: sustainable socio-ecological organizations

3. CA Approaches • CA is intuitive for representing processes that can be cast into uniform structure with varied behavior – e.g., land surface erosion • CA is used to represent non-cellular abstractions –e.g., restrictive for agent decision making • CA is often combined with other models using arbitrary data and control schemes – e.g., programming languages • Existing CA formalisms treat CA as a grey box • Initialize and peek at current state

4. Composable CA • ComposableCA extends the CA formalism to formally represent non-cellular model interactions • Benefits • Avoid ambiguous composition of CAs with other models through formal description of I/O relationships • Improve hybrid modeling for CA models • Support detailed representations of agent and landscape process interactions • Simplify model verification and simulation validation • Model interaction visibility

5. 2 1 0 y z x Composable CA Specification • Represented as a network, N, of cells (individual automata) • N =  XN , YN , D, {Mijk},T, F , where Mijk =  Xijk , Yijk , Qijk , Iijk ,ijk ,ijk ,T  F = { fin , fout } • Difference between multi-dimensional CA and two composed CCAs is in the mapping Distinguishes between internal and external I/O Specific mapping functions between cells and network as an entity