Matrix-Based Modeling of Discrete Event Systems under Event Insertion and Replacement Attacks

Abstract Existing research on discrete event system (DES) modeling and cybersecurity often lacks effective means to express events and dynamically characterize external attacks, thereby limiting the flexibility of security analysis. To overcome these limitations, this paper proposes a matrix-based event expression method that employs the semi-tensor product (STP) to convert auxiliary labels in DESs into a matrix form, leading to a more efficient mathematical characterization of dynamic behaviors. First, the event transmission capability of finite state machines (FSMs) is enhanced by formalizing event insertion and replacement between states as external attacks, thus improving the model's resilience against malicious interference. Subsequently, an external observation mechanism is designed to detect attacks during event transmission and quantify them via cost labels, thereby incorporating economic constraints into attacker behavior modeling. The results indicate that the proposed method improves the dynamic expressiveness of FSMs and supports the analysis and verification of DESs in cybersecurity contexts.