Cellular automata on graphs with random topologies where each node has k neighbors with k proportional to log(n) achieve consensus convergence time of O(log n / log log n), which is faster than high-dimensional grid topologies and represents the information-theoretic lower bound because the diameter of such graphs scales as log(n) / log(k-1)

In NKN's consensus protocol using cellular automata with random topology, malicious nodes achieve maximum disruption through the flip-side attack: setting their initial state to the minority opinion and never changing it, and the protocol is secure against this attack if and only if the fraction of malicious nodes is less than the absolute difference in honest node counts between the two states

NKN uses verifiable delay functions and blockchain-based randomness to generate node identities that cannot be controlled by attackers: a new node must first commit a transaction with proof-of-work, wait for several blocks (during which the node has no control over block producers), and then its identity is computed from the block hash of the block confirming its transaction, making it impossible to predict or grind for favorable positions