There are two main types of automata: simple and complex. Simple automata are a cybernetic system. This type of automata does not evolve with their environment. Communication is also of limited capacity, which is usually unidirectional. Simple automata are well defined and are considered a bounded system, i.e. a closed system. Since simple automata are a bounded system, emergent behavior does not exist within single automata, but emergence could be present within a cluster of cybernetic agents. This emergent behavior is quite limited in scope compared to complex automata.
Complex automata are evolving systems. Communication with internal and external environments is multi–directional for complex automata, due to their feedback loop properties. Complex automata have all the properties of complex adaptive systems: (a) simple rules for agents, ability to communicate with environment, to have stochastic functions within their decision making, and the ability to learn from doing. Complex automata are unbounded systems—actions are not defined completely to allow for emergent behavior. Since these automata are open systems, they are more adaptive to their environment and possess the ability to machine learn.
In terms of optimization problems, automata could roam around a state–space to determine possible solutions. Many of these financial applications are utilizing complex automata, e.g. ant algorithms, bee algorithms, and grasshopper algorithms. There are many variant automata algorithms but the main functions are similar—the automata is allowed to wander to find a solution that converges. These wandering complex automata are learning the solution landscape looking for a global optimum. Simple automata could be considered just calculators of certain tasks, but not actually learn from their environment.