Behavior of complemented CA whose complement vector is acyclic in a linear TPMACA

Since complemented cellular automata (CA) are nonlinear, the analysis of complemented CA is more difficult than that of linear CA. We present a detailed analysis of the behavior of complemented CA derived from a linear TPMACA. We especially investigate the behavior of complemented CA derived from a linear TPMACA C whose complement vector is an acyclic state lying on some nonzero tree of C.