Question: Consider a simple reflex agent maps a state to a single action. Suppose there exists a world with S states and A possible actions in

Consider a simple reflex agent maps a state to a single action. Suppose there exists a world with S states and A possible actions in any of these states. How many distinct simple reflex agents can exist in such a world? Or equivalently, how many functions f can there be for some f(s) = a?

Suppose each agent in the previous question is equipped with a memory so it can consider the previous k states and its current state when choosing an action. If we again assume that there are A possible actions per state, how many distinct simple reflex agents can exist with this modification?

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