\[ C_{i,t} = \begin{cases} 1 & \text{if cell } i \text{ is ON}_t\\ 0 & \text{if cell } i \text{ is OFF}_t \end{cases} \]
\[ \sum_{i \in \text{neighbor}} C_{i, t} \text{ } \in S \implies \text{ON}_{t+1} \] \[ \sum_{i \in \text{neighbor}} C_{i, t} \text{ } \notin S \implies \text{OFF}_{t+1} \]