Characterizing Configuration Spaces of Simple Threshold Cellular Automata

We study herewith the simple threshold cellular automata (CA), as perhaps the simplest broad class of CA with non-additive (i.e., non-linear and non-affine) local update rules. We characterize all possible computations of the most interesting rule for such CA, namely, the Majority (MAJ) rule, both in the classical, parallel CA case, and in case of the corresponding sequential CA where the nodes update sequentially, one at a time. We compare and contrast the configuration spaces of arbitrary simple threshold automata in those two cases, and point out that some parallel threshold CA cannot be simulated by any of their sequential counterparts. We show that the temporal cycles exist only in case of (some) parallel simple threshold CA, but can never take place in sequential threshold CA. We also show that most threshold CA have very few fixed point configurations and few (if any) cycle configurations, and that, while the MAJ sequential and parallel CA may have many fixed points, nonetheless...

• Type: Conference
• Year: 2004
• Where: ACRI
• Authors: Predrag T. Tosic, Gul Agha
• Keywords: ACRI 2004, Artificial Intelligence, Sequential, Simple Threshold, Threshold Ca