Node-Set Synchronization and Calculation of General Boolean Networks Combining STP and Q -Learning
研究了状态翻转控制下通用布尔网络的节点集同步问题，利用半张量积进行代数表示，并引入Q学习算法高效寻找最优翻转序列，实验显示成功率100%，优于传统方法的23.4%。
The calculation of the synchronization problem is a very important topic in the research of Boolean networks (BNs). This article focuses on the study of state-flipped control on the node-set synchronization problem of general BNs and incorporates reinforcement learning algorithms to enhance the calculation efficiency of the synchronization problem. First, the synchronized nodes are algebraically represented by the semi-tensor product (STP) of matrices, and the analysis of the BN for node-set synchronization under state-flipped control is given. Second, the sufficient and necessary conditions that can enable general BNs to realize node-set synchronization are derived. Meanwhile, an algorithm for finding the flip sequence is designed. In addition, this article develops a comprehensive calculation scheme connecting the recursive algorithm to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i>-learning for finding all the optimal paths. Finally, some cases are provided to verify the effectiveness of state-flipped control and the superiority of reinforcement learning in the calculation of synchronization problems. Numerical experiments demonstrate that the proposed reinforcement learning-based algorithm achieves up to 100% success rate in finding the optimal flip sequence, outperforming the traditional method (23.4% success rate), reducing the average flip action by 15%, and improving the scalability of large-scale networks.