This paper explores the generalized synchronization problem in one-dimensional cellular automata, focusing on algorithms that can synchronize a large-scale cellular automaton with an initial initiator at any position. The authors study various synchronization algorithms, including those proposed by Moore and Langdon, Varshavsky et al., Szwerinski, Settle and Simon, and Umeo et al. They propose a new eight-state optimum-step algorithm, which is the smallest known algorithm in this class. The paper also examines the state transition rule sets for these algorithms, testing their correctness and identifying redundant rules. Additionally, it discusses the complexity measures such as time, number of states, transition rules, filled-in ratio, symmetry, and state-change complexity. The authors provide computer implementations to verify the validity of the transition rule sets and compare the state-changes per cell across different algorithms. The paper contributes to the understanding of the generalized firing squad synchronization problem and offers new insights into the efficiency and design of synchronization protocols.This paper explores the generalized synchronization problem in one-dimensional cellular automata, focusing on algorithms that can synchronize a large-scale cellular automaton with an initial initiator at any position. The authors study various synchronization algorithms, including those proposed by Moore and Langdon, Varshavsky et al., Szwerinski, Settle and Simon, and Umeo et al. They propose a new eight-state optimum-step algorithm, which is the smallest known algorithm in this class. The paper also examines the state transition rule sets for these algorithms, testing their correctness and identifying redundant rules. Additionally, it discusses the complexity measures such as time, number of states, transition rules, filled-in ratio, symmetry, and state-change complexity. The authors provide computer implementations to verify the validity of the transition rule sets and compare the state-changes per cell across different algorithms. The paper contributes to the understanding of the generalized firing squad synchronization problem and offers new insights into the efficiency and design of synchronization protocols.