In order to create a rational planning agent, we need a way to mathematically express the given environment in which the agent will exist.

To do this, we must formally express a search problem $$ given our agent$$s current state $($its configuration within its environment$),$ how can we arrive at a new state that satisfies its goals in the best possible way? Formulating such a problem requires four things:

$1.$ A state space $$ The set of all possible states that are possible in the given world.

$2.$ A successor function $$ A function that takes in a state and an action and computes the cost of performing that action as well as the successor state, the state the world would be in if the given agent performed that action.

$3.$ A start state $$ The state in which an agent exists initially

$4.$ A goal state $$ A function that takes a state as input, and determines whether it is a goal state

When defining a state space, we distinguished the world state from a search state$$the former includes every last detail of the environment, and the latter keeps only the details needed for planning. You are asked to work on the missionaries and cannibals$$ problem stated as follows.

Three missionaries and three cannibals are on one side of a river, along with a boat that can hold only one or two people. Find a way to get everyone to the other side without leaving a group of missionaries in one place outnumbered by the cannibals in that place. Assume there is no way to send the boat across without at least one person in it$.$ Give the initial state, goal test, actions, transition model, and path cost function for this problem, making only those distinctions necessary to ensure a valid solution. Draw a diagram of the complete state space.