Vulnerability of AND/OR logic networks under cascading failures

Abstract

Cascading failures in AND/OR logic networks present a critical challenge in domains such as digital circuits and communication systems where reliability and resilience are paramount. This work investigates the vulnerability of AND/OR logic networks under cascading failures by examining the propagation mechanisms, failure modes, and robustness of such systems. In detail, we propose a hybrid fault propagation model based on the basic principles of AND/OR logic operations. Then, by utilizing both analytical and simulation approaches, we explore how initial localized disruptions can escalate through interconnected logical elements and lead to widespread system failures. Notably, it is shown that a Sigmoid function can be developed to quantify the vulnerability of the complex logic network. Moreover, the phase transition of the failures against the logic parameters is depicted and it is illustrated that the phase transition point is independent of the AND links. This study contributes to the understanding of cascading dynamics in logical networks and could facilitate design of feasible strategies for mitigating these vulnerabilities and recovering from substantial failures.