Grey Automata: Theory and Applications

In this paper, I introduce a novel paradigm called grey automata that integrates grey system theory with classical automata theory to model systems marked by uncertainty and incomplete information. I define grey automata by incorporating grey numbers interval based representations of uncertainty into state transitions, thus extending the conventional finite automata model. I establish the theoretical foundations of grey automata, demonstrating key properties such as closure under union, determinization, state equivalence, and minimality. Furthermore, I provide practical examples, including models for traffic light systems and vending machines, to illustrate the relevance and applicability of our approach in various real-world scenarios.