Here is pseudocode for three agent programs A, B, C:

In each of these agents, the function f is some arbitrary, possibly randomized, function of its inputs with no internal state of its own; the agent program runs on a computer with unbounded memory but finite clock speed. We’ll assume also that the environment and its performance measure are computable. 

a. Suppose the environment is fully observable, deterministic, discrete, single-agent, and static. For which agents, if any, is it the case that, for every such environment, there is some way to choose f such that the agent is perfectly rational? 

b. Suppose the environment is partially observable, deterministic, discrete, single-agent, and static. For which agents, if any, is it the case that, for every such environment, there is some way to choose f such that the agent is perfectly rational? 

c. Suppose the environment is partially observable, stochastic, discrete, single-agent, and dynamic. For which agents, if any, is it the case that, for every such environment, there is some way to choose f such that the agent is perfectly rational?

function A(percept) return fO function B(percept) return fB (percept) function C(percept) persistent: percepts, initially [] percepts push(percept,percepts) return fc(percepts)