probabilistic automata

Probabilistic automata are mathematical models used to describe systems that make decisions based on chance. They process input signals and, instead of moving to a fixed next step, they transition between states with certain probabilities. This means that given the same input, the system might behave differently each time, reflecting uncertainty or randomness. Such models are useful for analyzing systems where outcomes are not deterministic, like speech recognition or biological processes, helping us understand and predict behaviors that involve probabilistic outcomes in a structured way.