Adaptive Resilience via Probabilistic Automaton: Safeguarding Multi-Agent Systems from Leader Missing Attacks

Article Adaptive Resilience via Probabilistic Automaton: Safeguarding Multi-Agent Systems from Leader Missing Attacks Kuanxiang Wang 1 and Xin Gong 2,* 1 The School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China 2 The School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China * Correspondence: [email protected]; Tel.: +86-185-9806-0508 Received: 26 August 2024; Revised: 3 October 2024; Accepted: 18 October 2024; Published: 25 October 2024 Abstract: The resilience of leader-following structures has been a hotspot in both academic and industrial research. Existing studies mainly focus on maintaining follower coherence, usually assuming that the leader can always function properly. However, these studies neglect the risk of system paralysis if the leader is compromised. To resolve this problem, this paper leverages probabilistic automata grammar reasoning to investigate how followers can gradually infer their operational rules within the system over time. First, a grammatical inference module is implemented on the followers to enable them to deduce their rules once they receive commands from the leader. Then, this paper proposes three probabilistic automata reasoning methods for this inference: the Algorithm for Learning Regular Grammars with Inference Assistance (ALERGIA), Distinguished String Automata Inference (DSAI), and Minimum Divergent Inference (MDI). By using these methods, a follower can reason about deterministic finite automata from multiple commands issued by the leader, which are then utilized to construct deterministic probabilistic finite automata for representing the follower's rules. Finally, several examples are provided to validate the correctness of these reasoning methods and compare their efficiency in learning probabilistic automata. The results indicate that all three methods achieve an accuracy of 98.535% in learning the correct automata transformation function, and ALERGIA runs slightly faster. These findings suggest that even if the leader is compromised, the agent can still perform tasks autonomously using the inferred rules, thereby avoiding system paralysis.